MSC Induction 2010 - Intermediate Excel Exercises

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MSc Induction 2010 - Introduction to Basic

Students will have a wide range of Excel skills. Theare intended to ensure that all students acquire mi

skills that essential for all post graduate studies.To keep your own copy of the spreadsheet, save itwhich is your own filespace.

Good Excel skills will help you throughout the courquantitative material, and to complete courseworkgood Excel skills are an essential ingredient for a s

For those who are already competent in Excel, theintroduce some of the key concepts in investment,which you will need to know.

Excel has enormous capabilities. It is impossible toit can do in a few hours . However, these exercisesto get started: after that, the best way to learn is t

functions if you have a problem. Often, a Google san answer. For example, try Googling "portfolio op

This spreadsheet is laid out for self-completion atare getting through it very quickly, perhaps you cowho need some help.

This is the first year we have run Excel inductions i

suggestions for improvement would be most welco


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Intermediate Excel

se hands-on exercisesnimum data analysis

into the U: drive,

e to keep up with. More importantly,ccessful career.

exercises alsoand simple statistics,

teach you everythingwill give you enoughuse the built-in Help

arch will also produceimization in excel".

our own speed. If youuld find classmates

n this format,

me.


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The SpreadsheetA spreadsheet is a grid of cells. Each cell is uniquely identified by it cell address

You move the cursor around the spreadsheet by pointing and clicking with the m

Other keys and combinations also move around the sheet - Home to the top left

Entering Data and TextYou put information into a cell by highlighting with the cursor, typing numbers o

Enter the text / data in the green block into the blue block

UK Total Return % pa

Year Property Equities Bonds

2005 19.1 22.0 7.4

2006 18.1 16.8 -0.1

2007 -3.4 5.3 6.4

2008 -22.1 -29.9 15.0

2009 3.5 30.1 -0.3

Source: IPD, Ecowin

Data Formats

Data entries can be shown in a variety of formats - including the number of deci

Right-Click on a cell and pick Format Cells to see the range of options. You can c

Or you can pick some formats directly from the buttons on the Excel Home ribboOr you can enter cells directly in currency by putting a or $ or at the front of

Plus from Format Cells or the ribbon you can change the appearance of many fe

Data formats - format the blue cells so they look the same as the green

10.67 10.67 10.67 11 0.11 10.67% 11%

10.67 10.67 10.67 10.67 0.11 0.11 0.11

Cell appearance - format the blue cells so they look like the row above:

Cass Cass Cass Cass

Cass Cass Cass Cass


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Cell ranges, copy and move

Actions like formatting can be applied to blocks of cells at the same time.

Plus you can copy or move individual cells or blocks of cells to other locations, u

or Excel keyboard shortcuts Ctrl-C to copy Ctrl-V to paste, Ctrl-X Ctrl V to move.To select a block of cells, place the cursor in a corner of the block then Left-Click

or hold down Shift and use the Arrow keys to highlight the block.

Format the table on the right so it looks like the one below

Total Return % pa Total Ret

Year Property Equities Bonds Year Property

2005 19.1 22 7.4 2005 19.1

2006 18.1 16.8 -0.1 2006 18.1

2007 -3.4 5.3 6.4 2007 -3.4

2008 -22.1 -29.9 15 2008 -22.1

2009 3.5 30.1 -0.3 2009 3.5

Average 3.0 8.9 5.7 Average 3.04

Source: IPD, Datastream Source: IPD, Datastr

Then copy the table above to here And move the tab

There is much more you can do with formatting, including using built-in styles or

Explore the options on the Home Ribbon, and look at Cell Styles for examples.

Note you can also copy or move different attributes of c

And Format Painter on the Home Ribbon copies formats from one cell to others.

And you can repeat an effect such as changing format by hitting F4.


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You could have done all the formatting tasks above by u


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- the column (letters across the top) and row (numbers down the side).

ouse, or using the up/ down arrows or page up / down on the keyboard

, Ctrl-arrow to the end of the current block of entries etc

text, then hitting Enter, Up / Down arrows etc

al places shown, as currency values, in percentage format

hange the format of the current cell by from the menu.

n.a number, as a percentage by putting a % after a number.

tures of the entry - size and colour of text, alignment, cell background, borders around c

cells: use either R-Click Format Cells, or buttons from the Ribbon

5/21/2011 21May2011 May

5/21/2011 5/21/2011 5/21/2011

use either R-Click | Format Cells, or buttons from the ribbon

Cass

Cass


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ing the Cut-Copy-Paste buttons on the Home Ribbon

& Drag to highlight the block

rn % pa

Equities Bonds

22 7.4

16.8 -0.1

5.3 6.4

-29.9 15

30.1 -0.3

8.86 5.68

eam

le above to here

creating own.

lls - formulas, values, formatting - using Right-Click Paste Sp


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sing the Format Painter from the Home ribbon, or Copy | Righ


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ells etc


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cial.


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-Click | Paste Special | Formats.


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Arithmetic CalculationsThe primary purpose of a spreadsheet is to perform calculations. Within a simple

power from the ability to repeat and replicate calculations.

This section uses only basic arithmetic, and introduces the basic ideas of cell ref

The Arithmetic OperatorsThe four basic operators

Add Subtract Multiply Divide

Are entered using the Excel keys

+ - * /

A calculation can be entered directly into a cell by typing the arithmetic

So typing "+5+12+16/2" into a cell gives

But most often you produce calculated results from existing cells by using cell re

To calculate a result

put the cursor in the target cell and start the calculation by typing = o

add the cell references by typing in the Column / Row reference

or moving the cursor to the required cell after each operator using the

Do each of the following calculations

15 15 15 15

5 5 5 5

Order of calculation

Excel follows the standard rules for which operators are calculated first in a strin

The rule is calculate all multiplications and divisions, working from the left

Then calculate all additions and subtractions, working from the left

For example, calculate the string "+3+6x5+4/2-7" using the numbers i

= + x + / -

3 6 5 4 2 7

Note that doing multiplications and divisions first, this is worked out as 3 + 30 +

Add15+5

Subtract15-5

Multiply15x5

Divide 15/5

Total forRow


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If you do not want to follow the natural order of operations,

you have to indicate which parts of the calculation you want done first by includi

For example, calculate the string "(3+6)x(5+4)/(2-7)" using the numbe

= + x + / -

3 6 5 4 2 7

Note that with the brackets calculated first, this is worked out as 9 x 9 / -5 = 9 x

And calculate the string "=((3+6)x5)+(4/(2-7))" using the numbers in t

= + x + / -

3 6 5 4 2 7

Now the calculation is being worked out as (9 x 5) + (4 / -5) = 45 - 0.8

Powers and roots

Beyond the basic arithmetic, we can also calculate powers, square roots and oth

To raise a cell reference ColRow to the power n, type reference ColRow^n

For roots type reference ColRow^(1/n) - note the brackets round the division bit

Calculate each of the following

Squared

3 10 3.5 9 27

Repeated calculations by copying formulae

The power of spreadsheets starts to work when you have to repeat the same cal

on a large number of cells. Say I have the list of properties shown below:

with their values at the last two year ends

and their rental income, service charges and costs through the yearI need to calculate my rates of return for each one which is:

Income Return = (Rental Income + Service Charges - Costs)/Capital Va

Capital Growth = (Capital Value 2009 - Capital Value 2008)/Capital Val

Total Return = Income Return + Capital Growth

ie my total income through the year plus gain in capital value divided

to thePower 4

to thePower 12

squareroot

4th rootof


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Calculate returns for property 1 by putting the correct formulae in the

Note the return on the portfolio is worked out by applying the return ca

These are fairly typical returns for a set of UK buildings.

Prop # Capital Value 000 2009 000

2008 2009 Rental IncService C Costs1 1881 1966 144.8 73.4 30.1

2 552 509 40.3 8.8 12.1

3 1842 1512 105.0 18.4 38.7

4 1859 1608 78.1 27.9 27.9

5 1296 1072 90.7 46.7 15.6

6 1756 2221 110.6 12.3 40.4

7 656 585 38.0 19.7 19.0

8 838 1066 46.9 23.5 25.1

9 694 858 40.3 15.3 11.8

10 1305 1533 83.5 36.5 14.4

Total 12679 12930 778 282 235

Pinning cells - relative and absolute references

In the last example, the cell references in the formula changed automatically as

Sometimes you want to apply an input from one cell to a range of cells.

To do this, "fix" or "pin" the cell reference by putting $ signs in front of the colu

The $ signs can either be typed as you enter the pinned cell address, or hit F4 wi

You can pin both the row and column, so the same cell is used when the formula

In the blue cells, calculate the yellow cells multiplied by the green cell.

10.76

1 2 3 42 3 4 5

3 4 5 6

4 5 6 7


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In the blue cells, calculate the cells in each column multiplied by the gr

1 2 3 4

2 3 4 53 4 5 6

4 5 6 7

In the blue cells, calculate the cells in each row multiplied by the green

1 2 3 4

2 3 4 5

3 4 5 6

4 5 6 7


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grid structure, it gains its

rencing and copying calculations.

ferences

+

mouse or arrow keys

of calculations

green cells

2 -7


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ng them in brackets

s in the green cells

-1.8

e green cells

r roots

ulation

lue 2008

ue 2008

y initial capital value


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lue cells, then copy them down into the boxes.

lculations for the sum of all properties in row 90.

Income R Capital GrTotal Return %

you copied down.

n and row.

th the cursor over the cell

is copied across or down


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en cells in the top row

cells in the left column


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FunctionsExcel has many built-in functions which do more complicated calculations for you.

To see the complete list of functions, click the fx button in the entry bar above,

or Insert Function from the Formulas ribbon.

Functions also do other things, like conditional tests, sorting out data.

To use a function:

Put the cursor in the cell where you want the result of the function to appear.

if you know the name of the function, type =name, Excel will start to lis

or you can look up a function from the fx button or Formulas Insert Fun

typically, you complete a function by entering cell references, often sep

When the function name has been typed Excel provides hints as to what should b

or you can bring up a box with more information on how to fill out the function by

Getting help with a function

Note the link for help on this function which gives more explanation and worked e

(It is usually best to use the "Offline help from this computer" section of the help.

As an example, the block below contains a set of numbers, with simple statistics

-12 16 -3 7 9 22 Calculat

-9 -28 9 -45 -22 23

Type =functionname then Ctrl-A to see a full set of entri


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13 9 37 55 8 49

75 -13 38 -47 -22 -29

0 -22 -46 71 33 -48

0 -45 -3 30 42 -27

8 -20 -1 13 36 36

-29 -29 52 50 38 -23 Uses vari58 -32 66 -22 37 -6

26 -12 71 -30 45 25

-36 71 -35 57 44 63

Logical functions

Functions include the logic tests IF, AND, OR, NOT

You can use these to construct calculations which vary with values in the input ce

A cell has this formula

-1 0 =IF(C54>=0,1,0) Shows zero if yello

1 1 1 =IF(AND(C56>=0,D56>=0),1,0Shows 1 if both yell

5 5 =IF(C58>=0,D58,"") Shows value of yell

These conditional tests can be combined with logic statements to vary results if t

10 15 25=IF(AND(C60>=0,D60>=0),C60+D60,"")Adds yell

Exercise in Functions, Conditional Statements & Logic

Using the cells below and the blank space to the right, answer

for each asset class, in what % of years have returns b

for each asset class, what has been the average retur

in how many years have property returns been above

UK Total Return by Asset Class % pa

Property Equities Bonds T Bill

1947 0.7 -2.3 -14.3 0.5 9.1

1948 -6.5 -3.8 0.7 0.5 7.8

1949 -0.4 -5.8 -8.9 0.5 13.1

1950 14.3 10.9 4.0 0.5 0.3

For example, change the values in the yellow cells to see how results cha

InflationRPI


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1951 1.2 8.5 -9.6 0.5 15.9

1952 -2.6 -0.1 -0.8 2.1 9.1

1953 7.0 24.2 14.0 2.4 -6.3

1954 10.6 48.6 6.1 1.9 2.4

1955 0.7 10.9 -10.1 3.5 5.1

1956 6.1 -9.0 -3.2 5.0 4.91957 2.6 -1.1 -6.2 5.0 3.5

1958 8.1 47.9 17.0 5.1 3.4

1959 11.1 54.8 0.9 3.4 0.6

1960 9.8 1.8 -7.0 5.0 1.0

1961 6.3 1.7 -8.1 5.1 3.5

1962 6.9 0.4 24.7 4.5 4.2

1963 10.3 19.9 3.7 3.8 2.0

1964 8.3 -5.4 -2.3 4.4 3.3

1965 4.7 11.4 4.4 6.3 4.8

1966 3.2 -4.0 4.2 6.1 3.9

1967 7.9 34.3 2.6 5.9 2.5

1968 21.3 48.1 -2.4 7.4 4.7

1969 5.2 -11.9 0.2 7.9 5.4

1970 24.6 -3.5 3.6 7.5 6.4

1971 16.1 46.5 27.3 6.2 9.0

1972 29.3 16.4 -3.8 5.4 7.7

1973 28.4 -28.1 -8.9 9.0 10.6

1974 -15.9 -50.1 -15.2 12.6 19.1

1975 11.4 149.3 36.8 10.8 24.9

1976 9.4 2.3 13.7 11.3 15.1

1977 26.4 48.6 44.8 9.4 12.1

1978 25.6 8.6 -1.8 8.1 8.4

1979 22.8 11.5 4.1 13.5 17.2

1980 17.5 34.8 20.9 17.2 15.1

1981 15.0 13.6 1.8 13.8 12.1

1982 7.5 28.5 51.3 12.4 5.4

1983 7.6 28.8 15.9 10.1 5.3

1984 8.8 31.6 6.8 9.5 4.6

1985 8.3 20.2 11.0 11.9 5.7

1986 11.3 27.3 11.0 10.9 3.7

1987 26.0 8.0 16.3 9.6 3.7


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1988 29.5 11.5 9.4 11.0 6.8

1989 15.4 36.1 5.9 14.6 7.7

1990 -8.4 -9.7 5.6 15.9 9.3

1991 -3.1 20.7 18.9 11.6 4.5

1992 -1.6 20.5 18.4 9.5 2.6

1993 20.2 28.4 28.8 5.9 1.91994 11.9 -5.9 -11.3 5.4 2.9

1995 3.6 23.8 19.0 6.7 3.2

1996 10.0 16.7 7.7 6.2 2.5

1997 16.8 23.5 15.0 6.9 3.6

1998 11.8 13.8 19.4 7.9 2.8

1999 14.5 24.2 -3.2 5.5 1.8

2000 10.5 -5.9 9.8 6.2 2.9

2001 6.8 -13.3 3.9 5.5 0.7

2002 9.6 -22.7 10.3 4.1 2.9

2003 10.9 20.9 1.8 4.0 2.8

2004 18.3 12.8 6.6 4.5 3.5

2005 19.1 22.0 7.4 4.5 2.2

2006 18.1 16.8 -0.1 4.8 4.4

2007 -3.4 5.3 6.4 5.5 4.1

2008 -22.1 -29.9 15.0 3.0 0.9

2009 2.9 30.1 -0.3 0.6 2.4

Count

Average

% of Years

Sources: Scott The Property Masters, IPD, Barclays Capital Equity-Gilt Study


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.

t functions which match the name

tion

arated by commas

e entered,

hitting Ctrl-A.

xamples.

alculated from them in the blue Cells.

these stats for the whole block Calculate stats for the red values only - ent

=count(Range) =count(Range 1,Range 2)

es for each formula, as below.


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=sum(Range) =sum(Range 1,Range 2)

=average(Range) =average(Range 1,Range 2)

ation on these functions, xxxxif, to calculate values only for cells greater than=countif(Range,">0") note to type these functions

=sumif(Range,">0") the conditions is entered in quotes eg ">0"

=averageif(Range,">0")

lls.

cell 0

w cells>0

w cell if yellow cell>0, otherwise shows blank

o or more conditions are true, as below

w cells if both >0, otherwise shows blank

he following questions:

een above inflation? (Hint: Cell 58 above)

in those years when returns were above inflation? (Hint: average of the result

onds but below equities? (Hint: a bit like Cell D61 above.)

Returns if Return > Inflation Property return if return above bonds,

Property Equities Bonds T Bill

ge in blue cells:


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er blocks separated by comma


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.

from the above)

elow equities


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Statistical FunctionsExcel calculates a lot of standard statistics and statistical tests. Click fx an

This section uses just a few of them to generate the main indicators used

It works up to a very basic answer to one of the most important questions:

A set of descriptive statistics - the standard indicators for any data series -

Click Data Analysis from the Data ribbon, select Descriptive Stati

(Note if Data Analysis is not there, click the round Excel button top left an

You can make the resulting table neater by deleting the sections

If you don't know what the statistics mean, look them up in Googl

USA Total Returns by Asset Class, % pa

Property REITS Equities Bonds T Bill

1990 2.3 -17.3 -2.1 8.1 8.4

1991 -5.6 35.7 31.3 17.6 7.7

1992 -4.3 12.2 7.4 7.7 5.5

1993 1.4 18.5 10.1 13.0 3.4

1994 6.4 0.8 2.0 -5.8 3.0

1995 7.5 18.3 38.2 23.0 4.3

1996 10.3 35.8 24.1 1.3 5.5

1997 13.9 18.9 34.1 10.6 5.1

1998 16.2 -18.8 30.7 12.6 5.1

1999 11.7 -6.5 22.4 -5.6 4.82000 12.5 25.9 -12.5 15.2 4.7

2001 6.4 15.5 -12.0 6.6 5.9

2002 6.1 5.2 -22.7 15.2 3.4

2003 9.9 38.5 29.1 2.0 1.6

2004 13.1 30.4 10.7 4.8 1.0

2005 19.2 8.3 5.7 2.6 1.4

2006 15.0 34.4 15.3 2.6 3.2

2007 14.3 -17.8 6.0 10.3 4.82008 -7.4 -37.3 -37.1 17.9 4.5

2009 -17.1 27.4 27.1 -5.7 1.4

Sources: NCREIF, IPD, NAREIT, EcoWin


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Average and Annualised Returns

Investing over several periods, I am interested in how much the investme

The arithmetic average of returns over the periods does not show that, as

In year 1, the value of 100 invested has risen to 125 = 100 x 25/100

In year 2, the value of the investment has fallen to 93.75 = 125 x 25/

So over the two years, there has been a loss of 6.25, or a total loss of

The arithmetic average return is zero, which clearly does not show the fin

To calculate the overall change in value, we need to calculate a compoun

The compounded return is also know as Annualised Return, and is calculat

100 100

Year 1 25 25 125 = E62 x (1 + C63/1 Note if th

Year 2 -25 31 93.75 = E63 x (1 + C64/1 we would

0.0 -3.2 this uses the Excel Rate function

the Rate function is



AnnualReturn

Returnon 100

ReturnIndex

AverageReturn

Annualised Return


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1990 2.3 -17.3 -2.1 8.1 8.4

1991 -5.6 35.7 31.3 17.6 7.7

1992 -4.3 12.2 7.4 7.7 5.5

1993 1.4 18.5 10.1 13.0 3.4

1994 6.4 0.8 2.0 -5.8 3.0

1995 7.5 18.3 38.2 23.0 4.31996 10.3 35.8 24.1 1.3 5.5

1997 13.9 18.9 34.1 10.6 5.1

1998 16.2 -18.8 30.7 12.6 5.1

1999 11.7 -6.5 22.4 -5.6 4.8

2000 12.5 25.9 -12.5 15.2 4.7

2001 6.4 15.5 -12.0 6.6 5.9

2002 6.1 5.2 -22.7 15.2 3.4

2003 9.9 38.5 29.1 2.0 1.6

2004 13.1 30.4 10.7 4.8 1.0

2005 19.2 8.3 5.7 2.6 1.4

2006 15.0 34.4 15.3 2.6 3.2

2007 14.3 -17.8 6.0 10.3 4.8

2008 -7.4 -37.3 -37.1 17.9 4.5

2009 -17.1 27.4 27.1 -5.7 1.4

Sources: NCREIF, IPD, Datastream

Avera

Annualise

From these results alone, it looks like REITs and equities have been the be

But in investment we are also concerned about how variable the investme

For similar rates of return, we are more confident year to what what the in

And we are more likely to avoid catastrophes such as the 50% fall in the v

Risk and Standard DeviationIt is clear from the charts that returns on equities and REITs have gone up

50.0

US Returns % pa

1


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To get a numerical measure of variability, we calculate how much annual

Simply adding the differences would cancel out pluses and minuses. So to

We then add up the total squared differences to get "total difference" and

The Excel functions =varp and for variance and =s

1 2 3 4 5

1990 -2.1 10.4 -12.5 155.51991 31.3 10.4 20.9 438.5

1992 7.4 10.4 -3.0 9.1

1993 10.1 10.4 -0.3 0.1

1994 2.0 10.4 -8.4 70.4

1995 38.2 10.4 27.8 772.9

1996 24.1 10.4 13.7 186.8

1997 34.1 10.4 23.7 561.7

1998 30.7 10.4 20.3 413.6

1999 22.4 10.4 12.0 143.9

2000 -12.5 10.4 -22.9 525.4

2001 -12.0 10.4 -22.4 502.6

2002 -22.7 10.4 -33.1 1095.3

2003 29.1 10.4 18.7 350.6

2004 10.7 10.4 0.3 0.1

2005 5.7 10.4 -4.7 21.8

Annual average difference is a statistic called Variance. To bring that to

This gives a statistic called Standard Deviation, the most common mea

EquityReturn

AverageReturn

Difference from

AverageDifferenceSquared

1990

199

1

199

2

1993

199

4

1995

1996

199

7

1998

1999

2000

200

1

200

2

2003

200

4

2005

2006

200

7

2008

2009

-50.0

-40.0

-30.0-20.0

-10.0

0.0

10.0

20.0

30.0

40.0

Property

REITS

Equities

Bonds

T Bill

%

p[a

1

A

xisTitle

1990

199

1

199

2

1993

199

4

-60.0

-40.0

-20.0

0.0

20.0

40.0

60.0


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2006 15.3 10.4 4.9 24.3

2007 6.0 10.4 -4.4 19.0

2008 -37.1 10.4 -47.5 2258.4

2009 27.1 10.4 16.8 280.8

Formula Calculated

Variance ### Variance 391.5289Standard Deviation 19.7871 Standard Deviation 19.7871

Risk Adjusted Returns and Sharpe Ratio

We now have two performance measures for each asset: returns (good) a

To reduce the comparison of assets to a single measure, we need to asse

The most common indicator used is the Sharpe Ratio

Sharpe Ratio = (Average Return on A

The logic is the the T Bill - a fixed interest loan to the US Government oveFor any other, risky, investment, the question is how much extra return o

Thus the Sharpe Ratio is the return per unit of risk: a higher Sharpe Ratio i

A negative Sharpe Ratio - a return on a risky asset below T Bill - is lousy.

Calculate return, risk and Sharpe Ratio for each asset class over t



1990 2.3 -16.3 -2.1 8.1 8.4

1991 -5.6 58.4 31.3 17.6 7.7

1992 -4.3 23.5 7.4 7.7 5.5

1993 1.4 22.1 10.1 13.0 3.4

1994 6.4 8.4 2.0 -5.8 3.0

1995 7.5 22.3 38.2 23.0 4.3

1996 10.3 42.8 24.1 1.3 5.5

1997 13.9 23.7 34.1 10.6 5.1

1998 16.2 -17.5 30.7 12.6 5.1

1999 11.7 -4.4 22.4 -5.6 4.8

2000 12.5 30.4 -12.5 15.2 4.7

2001 6.4 10.1 -12.0 6.6 5.9

2002 6.1 2.0 -22.7 15.2 3.4

2003 9.9 37.0 29.1 2.0 1.6

2004 13.1 33.8 10.7 4.8 1.0

2005 19.2 12.4 5.7 2.6 1.4


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2006 15.0 36.7 15.3 2.6 3.2

2007 14.3 -16.4 6.0 10.3 4.8

2008 -7.4 -39.6 -37.1 17.9 4.5

2009 -17.1 25.0 27.1 -5.7 1.4

Sources: NCREIF, IPD, Datastream

Last 20 years


Average Return

(Standard Deviation) use the f

Sharpe Ratio = (Avera

1990-1999


Average Return

(Standard Deviation)

Sharpe Ratio

2000-2009


Average Return

(Standard Deviation)

Sharpe Ratio

The Sharpe Ratios look quite bad for property: only equities 2000-2009 ha

If I had been investing money in only one asset over the period, it would n

But there is one further key feature of an investment to be considered.

Portfolio Diversification

Diversification is the reduction in risk which can be achieved by combinin

Diversification reduces risk to the extent that returns on different assets d

Consider an extreme example of two risky assets for which returns always

The return on a combined portfolio of assets is the sum of (Asset Weight x

Clearly, we get a portfolio with the average return of the two assets and z

Investment Portfolio

% Weights

Asset 1 Asset 2


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50% 50%

Annual returns: Contribution to Return

Asset 1 Asset 2 Asset 1 Asset 2

1971 1.06 2.94 0.53 1.47

1972 1.20 2.80 0.60 1.40

1973 2.08 1.92 1.04 0.961974 2.88 1.12 1.44 0.56

1975 2.87 1.13 1.44 0.56

1976 2.06 1.94 1.03 0.97

1977 1.19 2.81 0.60 1.40

1978 1.07 2.93 0.53 1.47

1979 1.80 2.20 0.90 1.10

1980 2.72 1.28 1.36 0.64

1981 2.97 1.03 1.49 0.51

1982 2.34 1.66 1.17 0.83

1983 1.39 2.61 0.70 1.30

1984 1.00 3.00 0.50 1.50

1985 1.53 2.47 0.77 1.23

Avg Return 1.88 2.12 Avg Return

Std Deviation 0.71 0.71 Std Deviation

Diversification and CorrelationIn practice, we do not find assets with returns which offset each other ver

But there are some diversification benefits from assets which do not move

To measure diversification benefit, we need a numerical measure of the e

To do this, we first measure the difference in return for each asset each y

If both assets are above or below their own average at the same time, all

And multiplying the differences from their own average will be either plus

If one asset is above the other below their average in the same year, the

So assets which move together will generate a large positive sum of the p

To reduce covariance to a scale which does not depend on the units of me

Correlation = +1: the two variables move up and down at exa

Correlation = -1: the two variables move up and down opposit

Correlation = 0: there is no association at all between the two

The average sum of the produce of differences - Step 3, covariance - is t

This gives the standard measure of association, correlation, which alwa


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Of course, the covariance and correlation statistics can be calculated strai

Covariance is =covar(Range 1, Range 2Corre

US Returns % pa Average Return

Property Equities Property Equities1990 2.3 -2.1 6.6 10.4

1991 -5.6 31.3 6.6 10.4

1992 -4.3 7.4 6.6 10.4

1993 1.4 10.1 6.6 10.4

1994 6.4 2.0 6.6 10.4

1995 7.5 38.2 6.6 10.4

1996 10.3 24.1 6.6 10.4

1997 13.9 34.1 6.6 10.41998 16.2 30.7 6.6 10.4

1999 11.7 22.4 6.6 10.4

2000 12.5 -12.5 6.6 10.4

2001 6.4 -12.0 6.6 10.4

2002 6.1 -22.7 6.6 10.4

2003 9.9 29.1 6.6 10.4

2004 13.1 10.7 6.6 10.4

2005 19.2 5.7 6.6 10.4

2006 15.0 15.3 6.6 10.4

2007 14.3 6.0 6.6 10.4

2008 -7.4 -37.1 6.6 10.4

2009 -17.1 27.1 6.6 10.4

Covariance 25.41

Correlation 0.14

So we may include in a portfolio assets which do not have very attractive


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but which do reduce risk in the portfolio because they have low correlatio



1990 2.3 -17.3 -2.1 8.1 8.4

1991 -5.6 35.7 31.3 17.6 7.71992 -4.3 12.2 7.4 7.7 5.5

1993 1.4 18.5 10.1 13.0 3.4

1994 6.4 0.8 2.0 -5.8 3.0

1995 7.5 18.3 38.2 23.0 4.3

1996 10.3 35.8 24.1 1.3 5.5

1997 13.9 18.9 34.1 10.6 5.1

1998 16.2 -18.8 30.7 12.6 5.1

1999 11.7 -6.5 22.4 -5.6 4.8

2000 12.5 25.9 -12.5 15.2 4.7

2001 6.4 15.5 -12.0 6.6 5.9

2002 6.1 5.2 -22.7 15.2 3.4

2003 9.9 38.5 29.1 2.0 1.6

2004 13.1 30.4 10.7 4.8 1.0

2005 19.2 8.3 5.7 2.6 1.4

2006 15.0 34.4 15.3 2.6 3.2

2007 14.3 -17.8 6.0 10.3 4.8

2008 -7.4 -37.3 -37.1 17.9 4.5

2009 -17.1 27.4 27.1 -5.7 1.4

Calculate in the blue cells the correlations between asset returns

note you can do this either using the =correl function, or Data Analysis | C

Correlation with:


Property 1.00 0.02 0.14 -0.05 -0.14

REITS 0.02 1.00 0.47 -0.17 -0.28

Equities 0.14 0.47 1.00 -0.18 -0.04

Bonds -0.05 -0.17 -0.18 1.00 0.39

T Bill -0.14 -0.28 -0.04 0.39 1.00

How much of each asset in a Portfolio?

Having got this far, we can produce a very basic answer to one of the bigg


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My aim is not simply to bet everything on the asset with the highest retur

And because by diversifying across assets with low correlations, I can red

A simple way of stating the aim is to hold a mix of assets which produces

Below, first calculated a return on a mixed asset portfolio initially

This is done by multiplying returns for each asset by the weight iThen calculate the returns, risks and Sharpe Ratio for each asset

Then use the Excel Data | Solver tool to find the combination of a

If the Solver conditions are not already set up, you need to:

produce the maximum value of the Portfolio Sharpe Ratio in C

by varying the block of asset weights in Cells J356 to N356

subject to the constraint that none of that block of cells is less

Note we do not believe this is the right answer, because we think

and because this is the just the way things have turned out in the


Average Return 6.6 11.4 10.4 7.7 4.2

Risk (Std Deviation) 9.0 21.1 19.8 8.0 1.9

Sharpe Ratio 0.26 0.34 0.31 0.43 0.00


1990 2.3 -17.3 -2.1 8.1 8.4

1991 -5.6 35.7 31.3 17.6 7.7

1992 -4.3 12.2 7.4 7.7 5.5

1993 1.4 18.5 10.1 13.0 3.4

1994 6.4 0.8 2.0 -5.8 3.0

1995 7.5 18.3 38.2 23.0 4.3

1996 10.3 35.8 24.1 1.3 5.5

1997 13.9 18.9 34.1 10.6 5.1

1998 16.2 -18.8 30.7 12.6 5.1

1999 11.7 -6.5 22.4 -5.6 4.8

2000 12.5 25.9 -12.5 15.2 4.7

2001 6.4 15.5 -12.0 6.6 5.9

2002 6.1 5.2 -22.7 15.2 3.4

2003 9.9 38.5 29.1 2.0 1.6

2004 13.1 30.4 10.7 4.8 1.0


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2005 19.2 8.3 5.7 2.6 1.4

2006 15.0 34.4 15.3 2.6 3.2

2007 14.3 -17.8 6.0 10.3 4.8

2008 -7.4 -37.3 -37.1 17.9 4.5

2009 -17.1 27.4 27.1 -5.7 1.4


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d the category "Statistical" to see the full list.

o measure investment performance.

how much money should an investor put into different assets?

can be generated simply.

tics, highlight the green cells as Input Range, then A30 as output range, a

follow the steps shown to the right.)

ith repeated labels.

e.


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t is worth at the end, measured in return per year.

illustrated below.

, a gain of 25

00, a loss of 31

7.25%.

l change in value.

ed return from a Return Index.

ed in Excel with =rate

e returns were entered as % in the form 0.25

not need to divide returns by 100 to generate the Index.

to calculate the compounde rate over 2 years which leaves 93.75 from an initial 10

= rate(Number of Years,,-Initial Index Value,Final In

In the blue cells, calculate a return index for each asset

USA Total Returns by Asset Class, Indices 1989=100


1989 100 100 100 100 100


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1990

1991

1992

1993

1994

19951996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

In the blue cells, calculate average and annualised returns for eac

e Return use =average applied to col

d Return use =rate as shown in Cell

Note that annualised returns are typically a little less than average returns

st investments, T Bills and property the worst.

nt returns are.

vestment will be worth if returns are less variable.

alue of REITs from 2006 to 2008.

and down much more than other assets.

20

US Return Index 1989 = 100


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eturns have varied from their own average - the figures and bars in red below.

get risk of the minus signs, we first square the differences.

divide by the number of years to get "annual average difference" at the bottom of

devp for standard deviation do all these steps at once dir

figure on the same scale as the average, we take the square root of the variance.

ure of investment risk.

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

20

40

60

80

00

Property

REITS

Equities

Bonds

T Bill

1996

199

7

1998

1999

2000

200

1

200

2

2003

200

4

2005

2006

200

7

2008

2009

Differencefrom Average

Equity Return

Average Return


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d risk (bad).

s both return and risk at the same time.

set - Average Return on T Bill) / Standard Deviation

a short period - is the most certain investment I can buy.er a T Bill does it offer for the extra risk?

s better.

he periods indicated.


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nction =stdevp(Range of Annual Returns)

ge Return on Asset - Average Return on T Bill) / Standard Deviation of Asset

ve a lower result.

ot have been property.

assets in a portfolio.

o not move up and down together.

move in opposite directions.

Asset Return).

ro risk - an infinite Sharpe Ratio


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Portfolio

2.00

2.00

2.002.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

0.00

strongly.

exactly in line with each other.

tent to which asset returns are linked.

ar from its own average (Step 2), and multiply them together (Step 2).

he observations in the chart will fall in the top right or bottom left quadrants.

times plus or a minus times minus - that is, a positive number.

product will be a minus number.

roduct of differences, the opposite a large negative.

asurement, covariance is divided by the product of the standard deviations of the t

ctly the same times (but not necessarily by the same amounts).

e to each other.

variables.

erefore an indicator of overall association in the two series.

ys has a value between +1 and -1.

19

71

19

72

19

73

19

74

19

75

19

76

19

77

19

78

19

79

19

80

19

81

19

82

19

83

19

84

19

85

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

Asset and Portfolio Returns

Asset 1

Asset 2

Portfolio

%

pa


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ght off the original figures, as in Cells C287 and C288.

lation is =correl(Range 1, Range 2)

Step 1 Step 2

Difference from Average Product of

Property Equities Differences-4.3 -12.5 53.6

-12.2 20.9 -255.2

-10.9 -3.0 32.8

-5.2 -0.3 1.6

-0.2 -8.4 1.8

0.9 27.8 26.2

3.7 13.7 50.7

7.3 23.7 173.39.7 20.3 196.4

5.1 12.0 61.2

5.9 -22.9 -134.5

-0.2 -22.4 5.2

-0.5 -33.1 16.0

3.3 18.7 61.4

6.6 0.3 2.1

12.6 -4.7 -58.7

8.4 4.9 41.4

7.7 -4.4 -33.7

-14.0 -47.5 663.7

-23.7 16.8 -397.1

Step 3

Sum of Product 508.28

Number of Observations 20

Step 3

Covariance 25.41

Std Dev Property 9.04

Std Dev Equities 19.79

Step 4

Correlation 0.14

eturns and risks in their own right,

-30.0 -25.0 -20.0 -15.0 -10.0 -5.0

-60.0

-40.0

-20.0

0.0

20.0

40.0

Differences f

US Property

USE

quities


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s with other assets.

in the green cells.

orrelation from the Data ribbon

est questions in finance: how should I spread my money over different assets?


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s, because is also likely to have the highest risk

ce risk without sacrificing returns, or at modest cost in returns.

he best risk adjusted return - the highest Sharpe Ratio.

assuming and equal weight in each asset class.

the blue cells in Cols J to N, and adding the results in column O.nd for the portfolio in the blue rows 345 to 347.

set weights which produces the maximum Sharpe Ratio on the portfolio.

ell O354

than 0.

the way property returns is measured understates their risk,

past, which may not be the same in the future.

Portfolio

8.2

5.7

0.69

Property REITS Equities Bonds T Bill Portfolio

Weights 23% 13% 9% 55% 0% 100%

1990 0.5 -2.2 -0.2 4.5 0.0 2.6

1991 -1.3 4.5 2.9 9.8 0.0 15.9

1992 -1.0 1.5 0.7 4.3 0.0 5.5

1993 0.3 2.3 0.9 7.2 0.0 10.8

1994 1.5 0.1 0.2 -3.2 0.0 -1.5

1995 1.7 2.3 3.5 12.7 0.0 20.3

1996 2.3 4.5 2.2 0.7 0.0 9.8

1997 3.2 2.4 3.1 5.9 0.0 14.6

1998 3.7 -2.4 2.8 6.9 0.0 11.1

1999 2.7 -0.8 2.1 -3.1 0.0 0.8

2000 2.8 3.3 -1.2 8.4 0.0 13.4

2001 1.5 2.0 -1.1 3.6 0.0 5.9

2002 1.4 0.7 -2.1 8.4 0.0 8.3

2003 2.3 4.9 2.7 1.1 0.0 10.9

2004 3.0 3.8 1.0 2.6 0.0 10.5


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2005 4.4 1.0 0.5 1.4 0.0 7.4

2006 3.4 4.3 1.4 1.5 0.0 10.6

2007 3.3 -2.3 0.6 5.7 0.0 7.2

2008 -1.7 -4.7 -3.4 9.9 0.0 0.1

2009 -3.9 3.5 2.5 -3.2 0.0 -1.1


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nd check Summary Statistics


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dex Value)


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h asset

ls C to G

67 applied to Cols J to N


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ol 5.

ect from the original figures, as at the bottom of Col


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of Asset


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o series (Step 4).


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0.0 5.0 10.0 15.0

rom Average R


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Check these boxes, then OK


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Compounding Interest & InvestmenThe foundation of valuation, investment decisions and performance measure

Consider the simplest investment question: what is the value at any point in t

a sum of money a - the principal - invested now

at a constant rate of interest (or return) r

at each point in the future n

assuming the interest (return) received is paid each year and the ye

Each year, we calculate interest on the accumulated amount and add it into th

Principle a = 1

Interest Rate r = 5%

Year

0 1 2 3 4 5 6

Interest 0.05 0.05 0.06 0.06 0.06 0.06

Total Value 1 1.05 1.10 1.16 1.22 1.28 1.34

We can cut out a stage of this, and calculate the value of the investment each

or Future Value Year n = Future Value Year n-1 x

Year = n

0 1 2 3 4 5 6

Future Value 1.00 1.05 1.10 1.16 1.22 1.28 1.34

or Future Value 1.00 1.05 1.10 1.16 1.22 1.28 1.34

There are many variants around this basic idea, to do with interest paid at diff

and to accommodate a fixed amount invested in each period rather than a lu

DiscountingDiscounting is the flip side of compounding. It asks how much do I need to inv

Or alternatively, how much will I pay today to receive x at some point in the

Assume there is an investment with a fixed rate of interest and no risk of loss

If the interest rate on this riskless investment is 5%, to have 1 in one year's ti

Investment Today x (1 + 5%) = Future Value oso

Future Value (FV) = a x (1 + r)n


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Investment Today = Future Value 0.95

And we can use the same formula to determine how much needs to be investe

By convention, the amount we need to invest today is called Present Value

Future Value 1

Interest Rate 5%

Year = n

0 1 2 3 4 5 6

Present Value 1.00 0.95 0.91 0.86 0.82 0.78 0.75

So this tells us that the Present Value of 1 in 100 years time if the interest ra

The Required Rate of Return, Discount Rate

Assume the least risky form of investment available - lending to the Governm

A Government Bond (UK Gilt), for example, pays a guaranteed amount of inter

So a 100 Bond maturing at the end of 2015 with a Coupon of 5% will pay 5 i

Other forms of investment are risky. For equities, I don't know how much divid

for a property, I dont know whether my tenants will go bankrupt, whether I wil

To compensate for the added risk, I will require an extra rate of return on the i

A bond issued by a blue-chip company (Tesco, Nestle) might be regarded as n

A speculative office development in Russia would clearly be a very risky inves

The extra return I require over the risk free rate is know as the risk premium

Required Return for Risky Investment = Risk F

Every specific investment will have its own risk premium. I would assume that

Cash Flows and Discount Rates - Discounted Cash flow (DCF)

The investment decision is how much am I prepared to pay today for an invest

The investment process is therefore always:

what is the best estimate of the future payments expected from the

how much more risky is that future stream of payments than an inv

therefore what is my required return estimated from risk free rate +

what is the Present Value of the expected cash flow discounted by t

For example, how much will I bid to buy a property which I expect to generate

Present Value (PV) = Future Value / (1 + r)n


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and I estimate I will be able to sell for 625,000 at the end of five years, if my

Required Return RR (Discount Rate) 7.50%

Annual Rent 50,000

Expected Sale Price 625,000

Year

0 1 2 3 4 5

Income 50,000 50,000 50,000 50,000 50,000

Capital ###

et Cash Flow (NCF) 0 50,000 50,000 50,000 50,000 ###

resent Value of 1 1.000 0.930 0.865 0.805 0.749 0.697= 1 / (1 +

PV of Cash Flow 0 46,512 43,267 40,248 37,440 ### = NCF x

Total PV ### =sum(PV of Cash Flow)

So the calculation tells me that my best estimate of the maximum I should pa

Discounted Cash Flow and Net Present Value (NPV)

Another way of setting out the Discounted Cash Flow calculation is to include t

of the investment as a negative cash flow (ie payment) in Year 0 (ie now)

So below we put in the price I can afford to pay as -637,643 in Year 0.

The sum of cash flows - Net Present Value (NPV) - is now 0: the investment will

my initial purchase price plus a rate of return appropriate my estimate of the r


Annual Rent 50,000


Year

0 1 2 3 4 5

Income 50,000 50,000 50,000 50,000 50,000

Capital ### ###

et Cash Flow (NCF) ### 50,000 50,000 50,000 50,000 ###

resent Value of 1 1.000 0.930 0.865 0.805 0.749 0.697= 1 / (1 +


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PV of Cash Flow ### 46,512 43,267 40,248 37,440 ###= NCF x

Net Present Value (NPV) 137,643by sum of cash flows

NPV by Excel function 137,643using Excel =npv(Required Return, Fu

We can also calculate NPV straight from the Required Return and Net Cash Flo

Note that if we put in an initial price less than 637,000 the NPV is positive - I

If we put in an initial price more than 637,000, the NPV is negative - a bad de

NPV - based on cash flows a lot more complicated that we show here - is one o

deciding whether to buy investments in all asset classes.

The decision rule is if my calculation shows NPV>=0, buy the investment, if N

Discounted Cash Flow and Internal Rate of Return (IRR)

Internal Rate of Return is the second common way of evaluating investments.

IRR is the actual rate of return I will get given the expected cash flows.

(An alternative way of saying the Discount Rate which will result in an NPV of

Now the decision rule is if IRR>= my Required Return buy the investment, if le


Annual Rent 50,000


Year

0 1 2 3 4 5

Income 50,000 50,000 50,000 50,000 50,000

Capital ### ###

et Cash Flow (NCF) ### 50,000 50,000 50,000 50,000 ###

resent Value of 1 1.000 0.930 0.865 0.805 0.749 0.697= 1 / (1 +

PV of Cash Flow ### 46,512 43,267 40,248 37,440 ###= NCF x

Net Present Value (NPV) 62,357by sum of cash flows

NPV by Excel function 62,357using Excel =npv(Required Return, Fu

IRR by Excel Function 5.2%


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Returnsent are a few basic concepts.

e future of

ar end and always reinvested

e investment.

7 8 9 10 11 12 13 14 15

0.07 0.07 0.07 0.08 0.08 0.09 0.09 0.09 0.10

1.41 1.48 1.55 1.63 1.71 1.80 1.89 1.98 2.08

year directly by the formula

(1 + r)

7 8 9 10 11 12 13 14 15

1.41 1.48 1.55 1.63 1.71 1.80 1.89 1.98 2.08

1.41 1.48 1.55 1.63 1.71 1.80 1.89 1.98 2.08

erent frequencies (at the start or end of periods, quarterly or monthly etc)

p sum at the start. Excel functions deal with all of these.

st today to have a sum of x in the future?

uture? Or another way, how much is x paid in the future worth today?

- a bond from a credit-worthy government is as close as we get.

ime we use the formula:

f x

01234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586878889909192939495969798991001011021031041051061071081091101111121131141151161171181191201211221231241251261271281291301311321331341351361371381391401411421431441451461471481491501511521531541551561571581591601611621631641651661671681691701711721731741751761771781791801811821831841851861871881819191911111

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,00020,000

Total Value of Investme

1.00

1.20

Prese


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d today to have 1 after a period of n years:

7 8 9 10 11 12 13 14 15

0.71 0.68 0.64 0.61 0.58 0.56 0.53 0.51 0.48

e is 5% is only 0.007.

nt at a fixed rate of interest - is 5%.

est, and a fixed payment on redemption.

n interest in each of the next 5 years, and a redemption payment of 100 in 2015.

ends they will pay, or what my share will be worth next week;

ll get new tenants at the end of leases, what I will be able to sell the property for.

nvestment.

early as low risk as the government, so my required return could be 5.2%.

ment, and my required return could be 25% or more.

ee Rate + Risk Premium

a fully let shopping centre in Germany is less risky than an office development in Du

ment which is expected to pay certain amounts in the future.

investment - the cash flow

stment in risk-free Government Bonds

risk premium

e required return.

50,000 per year in rent

0123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899101010101111111

0.00

0.20

0.40

0.60

0.80


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required return is 7.5%?

RR)^n

V of 1

for the building is 638,000.

he initial cost

l exactly pay back

isk: it is just a fair deal

RR)^n


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V of 1

ture Cash Flows) + Initial Cash Flow

ws using the Excel Function =npv

get back more than I need to compensate for risk, a good deal

al.

f the most common ways of

V


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16 17 18 19 20 21 22 23 24

0.10 0.11 0.11 0.12 0.13 0.13 0.14 0.15 0.15

2.18 2.29 2.41 2.53 2.65 2.79 2.93 3.07 3.23

16 17 18 19 20 21 22 23 24

2.18 2.29 2.41 2.53 2.65 2.79 2.93 3.07 3.23

2.18 2.29 2.41 2.53 2.65 2.79 2.93 3.07 3.23

0123495969798199200

nt

t Value


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16 17 18 19 20 21 22 23 24

0.46 0.44 0.42 0.40 0.38 0.36 0.34 0.33 0.31

ai.

1234560708091011112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200

Present Value


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25 26 27 28 29 30 31 32 33

0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24

3.39 3.56 3.73 3.92 4.12 4.32 4.54 4.76 5.00

25 26 27 28 29 30 31 32 33

3.39 3.56 3.73 3.92 4.12 4.32 4.54 4.76 5.00

3.39 3.56 3.73 3.92 4.12 4.32 4.54 4.76 5.00


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25 26 27 28 29 30 31 32 33

0.30 0.28 0.27 0.26 0.24 0.23 0.22 0.21 0.20


125/242


126/242


127/242

34 35 36 37 38 39 40 41 42

0.25 0.26 0.28 0.29 0.30 0.32 0.34 0.35 0.37

5.25 5.52 5.79 6.08 6.39 6.70 7.04 7.39 7.76

34 35 36 37 38 39 40 41 42

5.25 5.52 5.79 6.08 6.39 6.70 7.04 7.39 7.76

5.25 5.52 5.79 6.08 6.39 6.70 7.04 7.39 7.76


128/242

34 35 36 37 38 39 40 41 42

0.19 0.18 0.17 0.16 0.16 0.15 0.14 0.14 0.13


129/242


130/242


131/242

43 44 45 46 47 48 49 50 51

0.39 0.41 0.43 0.45 0.47 0.50 0.52 0.55 0.57

8.15 8.56 8.99 9.43 9.91 10.40 10.92 11.47 12.04

43 44 45 46 47 48 49 50 51

8.15 8.56 8.99 9.43 9.91 10.40 10.92 11.47 12.04

8.15 8.56 8.99 9.43 9.91 10.40 10.92 11.47 12.04


132/242

43 44 45 46 47 48 49 50 51

0.12 0.12 0.11 0.11 0.10 0.10 0.09 0.09 0.08


133/242


134/242


135/242

52 53 54 55 56 57 58 59 60

0.60 0.63 0.66 0.70 0.73 0.77 0.81 0.85 0.89

12.64 13.27 13.94 14.64 15.37 16.14 16.94 17.79 18.68

52 53 54 55 56 57 58 59 60

12.64 13.27 13.94 14.64 15.37 16.14 16.94 17.79 18.68

12.64 13.27 13.94 14.64 15.37 16.14 16.94 17.79 18.68


136/242

52 53 54 55 56 57 58 59 60

0.08 0.08 0.07 0.07 0.07 0.06 0.06 0.06 0.05


137/242


138/242


139/242

61 62 63 64 65 66 67 68 69

0.93 0.98 1.03 1.08 1.14 1.19 1.25 1.31 1.38

19.61 20.59 21.62 22.70 23.84 25.03 26.28 27.60 28.98

61 62 63 64 65 66 67 68 69

19.61 20.59 21.62 22.70 23.84 25.03 26.28 27.60 28.98

19.61 20.59 21.62 22.70 23.84 25.03 26.28 27.60 28.98


140/242


141/242


142/242


143/242

70 71 72 73 74 75 76 77 78

1.45 1.52 1.60 1.68 1.76 1.85 1.94 2.04 2.14

30.43 31.95 33.55 35.22 36.98 38.83 40.77 42.81 44.95

70 71 72 73 74 75 76 77 78

30.43 31.95 33.55 35.22 36.98 38.83 40.77 42.81 44.95

30.43 31.95 33.55 35.22 36.98 38.83 40.77 42.81 44.95


144/242

70 71 72 73 74 75 76 77 78

0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02


145/242


146/242


147/242

79 80 81 82 83 84 85 86 87

2.25 2.36 2.48 2.60 2.73 2.87 3.01 3.16 3.32

47.20 49.56 52.04 54.64 57.37 60.24 63.25 66.42 69.74

79 80 81 82 83 84 85 86 87

47.20 49.56 52.04 54.64 57.37 60.24 63.25 66.42 69.74

47.20 49.56 52.04 54.64 57.37 60.24 63.25 66.42 69.74


148/242

79 80 81 82 83 84 85 86 87

0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01


149/242


150/242


151/242

88 89 90 91 92 93 94 95 96

3.49 3.66 3.84 4.04 4.24 4.45 4.67 4.91 5.15

73.22 76.89 80.73 84.77 89.01 93.46 98.13 103.03 108.19

88 89 90 91 92 93 94 95 96

73.22 76.89 80.73 84.77 89.01 93.46 98.13 103.03 108.19

73.22 76.89 80.73 84.77 89.01 93.46 98.13 103.03 108.19


152/242

88 89 90 91 92 93 94 95 96

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01


153/242


154/242


155/242

97 98 99 100 101 102 103 104 105

5.41 5.68 5.96 6.26 6.58 6.90 7.25 7.61 7.99

113.60 119.28 125.24 131.50 138.08 144.98 152.23 159.84 167.83

97 98 99 100 101 102 103 104 105

113.60 119.28 125.24 131.50 138.08 144.98 152.23 159.84 167.83

113.60 119.28 125.24 131.50 138.08 144.98 152.23 159.84 167.83


156/242

97 98 99 100 101 102 103 104 105

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01


157/242


158/242


159/242

106 107 108 109 110 111 112 113 114

8.39 8.81 9.25 9.71 10.20 10.71 11.25 11.81 12.40

176.22 185.04 194.29 204.00 214.20 224.91 236.16 247.97 260.36

106 107 108 109 110 111 112 113 114

176.22 185.04 194.29 204.00 214.20 224.91 236.16 247.97 260.36

176.22 185.04 194.29 204.00 214.20 224.91 236.16 247.97 260.36


160/242

106 107 108 109 110 111 112 113 114

0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00


161/242


162/242


163/242

115 116 117 118 119 120 121 122 123

13.02 13.67 14.35 15.07 15.82 16.61 17.45 18.32 19.23

273.38 287.05 301.40 316.47 332.30 348.91 366.36 384.68 403.91

115 116 117 118 119 120 121 122 123

273.38 287.05 301.40 316.47 332.30 348.91 366.36 384.68 403.91

273.38 287.05 301.40 316.47 332.30 348.91 366.36 384.68 403.91


164/242

115 116 117 118 119 120 121 122 123

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


165/242


166/242


167/242

124 125 126 127 128 129 130 131 132

20.20 21.21 22.27 23.38 24.55 25.78 27.06 28.42 29.84

424.10 445.31 467.58 490.95 515.50 541.28 568.34 596.76 626.60

124 125 126 127 128 129 130 131 132

424.10 445.31 467.58 490.95 515.50 541.28 568.34 596.76 626.60

424.10 445.31 467.58 490.95 515.50 541.28 568.34 596.76 626.60


168/242

124 125 126 127 128 129 130 131 132

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


169/242


170/242


171/242

133 134 135 136 137 138 139 140 141

31.33 32.90 34.54 36.27 38.08 39.99 41.98 44.08 46.29

657.93 690.82 725.36 761.63 799.71 839.70 881.68 925.77 972.06

133 134 135 136 137 138 139 140 141

657.93 690.82 725.36 761.63 799.71 839.70 881.68 925.77 972.06

657.93 690.82 725.36 761.63 799.71 839.70 881.68 925.77 972.06


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133 134 135 136 137 138 139 140 141

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


173/242


174/242


175/242

142 143 144 145 146 147 148 149

48.60 51.03 53.58 56.26 59.08 62.03 65.13 68.39

### ### ### ### ### ### ### ###

142 143 144 145 146 147 148 149

### ### ### ### ### ### ### ###

### ### ### ### ### ### ### ###


176/242

142 143 144 145 146 147 148 149

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


177/242


178/242


179/242

150 151 152 153 154 155 156 157

71.81 75.40 79.17 83.13 87.28 91.65 96.23 101.04

### ### ### ### ### ### ### ###

150 151 152 153 154 155 156 157

### ### ### ### ### ### ### ###

### ### ### ### ### ### ### ###


180/242

150 151 152 153 154 155 156 157

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


181/242


182/242


183/242

158 159 160 161 162 163 164 165

106.09 111.40 116.97 122.82 128.96 135.41 142.18 149.28

### ### ### ### ### ### ### ###

158 159 160 161 162 163 164 165

### ### ### ### ### ### ### ###

### ### ### ### ### ### ### ###


184/242

158 159 160 161 162 163 164 165

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


185/242


186/242


187/242

166 167 168 169 170 171 172 173

156.75 164.59 172.82 181.46 190.53 200.06 210.06 220.56

### ### ### ### ### ### ### ###

166 167 168 169 170 171 172 173

### ### ### ### ### ### ### ###

### ### ### ### ### ### ### ###


188/242

166 167 168 169 170 171 172 173

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


189/242


190/242


191/242

174 175 176 177 178 179 180 181

231.59 243.17 255.33 268.09 281.50 295.57 310.35 325.87

### ### ### ### ### ### ### ###

174 175 176 177 178 179 180 181

### ### ### ### ### ### ### ###

### ### ### ### ### ### ### ###


192/242

174 175 176 177 178 179 180 181

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


193/242


194/242


195/242

182 183 184 185 186 187 188 189

342.16 359.27 377.23 396.10 415.90 436.70 458.53 481.46

### ### ### ### ### ### ### ###

182 183 184 185 186 187 188 189

### ### ### ### ### ### ### ###

### ### ### ### ### ### ### ###


196/242


197/242


198/242


199/242

190 191 192 193 194 195 196 197

505.53 530.81 557.35 585.21 614.48 645.20 677.46 711.33

### ### ### ### ### ### ### ###

190 191 192 193 194 195 196 197

### ### ### ### ### ### ### ###

### ### ### ### ### ### ### ###


200/242

190 191 192 193 194 195 196 197

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00


201/242


202/242


203/242

198 199 200

746.90 784.24 823.46

### ### ###

198 199 200

### ### ###

### ### ###


204/242

198 199 200

0.00 0.00 0.00


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Rental Cash Flows for PropertyFor a property investment, the most important element of the cash flow is rental

This section applies financial maths to a basic discounted cash flow in a format t

Rental incomes are governed by 3 key concepts:

Rent passing: the rent being paid by the tenant today, set

Market Rental Value (also Estimate or Open Market Rentallet at if let on the open market today. Market Rental Valu

mainly the state of the economy, vacancy rate and curren

Rent Review: an arrangement to vary the rent periodically

the Rent Passing is increased to Market Rental Value only

Lease Contract: the contract between landlord and tenant

So the information investors will be looking at to estimate future income from in

Assume we are looking at this building at the end of 2010.

Unit Lease Start Lease End

1 2006 2021 5 2011 21,800

2 2005 2020 5 2015 26,000

3 2009 2024 5 2014 25,070

We need to calculate the expected income from this property, and decide how

We will use a 5 year discounted cash flow, and assume that:

Market Rental Values will grow at 2.0%

My Required Return (Discount Rate) is 7.5%

The building can be sold at the end of 2015 for 1,400,000

In the blue cells below:

- calculate the market rental value at each year end,

- calculate the NPV of the investment assuming a pu

both by discounting the individual cash fl

- use Excel Data | What-If Analysis | Goal Seek to fin

2010 2011 2012 2013 2014

Year 0 1 2 3 4

Market Rental of a Unit 26,000

Rental Income (calendar years)

Unit 1 21,800

Unit 2 26,000

Unit 3 25,070

Total 72,870

Capital ###

RentReviewFrequency

Next RentReview atEnd:

RentPassing000


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Net Cash Flow

PV of 1 @ 7.5%

PV of Cash Flow

Net Present Value (NPV) sum of PV of Cash FlowNet Present Value (NPV) formula = NPV(Required Return,Future Cash Fl


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income. (There are others, such as landlords' costs we will ignore here.)

pical for UK property investment.

t the start of the lease or last rent review.

Value): the rent the building wouldvaries with the demand and supply -

t rate of development completions.

through the lease. In the UK, usually an Upward Only Rent Review -

if Market Rental Value is higher than Rent Passing - every 5 years.

hich runs for a specified term, in the UK usually from 5 to 15 years.

estments will be something like this. For simplicity all dates are at the year end

26,000

26,000

26,000

uch we might bid to buy it.

pa

and the income from each unit (rent reviews are indicated in yellow)

rchase price of 1m (shown as a negative cashflow in year 0)

ws and by using the Excel NPV function

the initial purchase price (in the red cell) which sets the NPV to zero

2015

5

Rental value with compound growth @ 2%

Rental income raised to market rental value after each review date (in y

Sum of unit rental incomes

1,400,000Assume sale at 1.4 million, purchase at end 2010 at -GUESS

MarketRentalValue 000


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Sum of Income & Capital

Net Cash Flow x PV of 1

ws) + Year 0 Cash Flow

formula 1 / (1 + Required Return)^Year Number


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ellow)


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Rental Cash Flows for Property

For a property investment, the most important element of t

Rental incomes are governed by 3 key concepts:

Rent passing: the rent being paid by the tenant to

Market Rental Value (also Estimate or Open Markelet at if let on the open market today. Market Re

mainly the state of the economy, vacancy rate a

Rent Review: an arrangement to vary the rent peri

the Rent Passing is increased to Market Rental V

Lease Contract: the contract between landlord an

So the information investors will be looking at to estimate fu

Assume we are looking at this building at the end of 2010.

Unit

1 2006 2021 5 2011 21800

2 2005 2020 5 2015 26000

3 2009 2024 5 2014 25070

We need to calculate the expected income from this propert

We will use a 5 year discounted cash flow, and assume that:

Market Re 0.02

My Requir 0.08

The buildi 1400000

In the blue cells below:

- calculate the market rental value at each year e

- calculate the NPV of the investment assuming a

both by discounting the individual cash

- use Excel Data What-If Analysis Goal Seek to fin

2010 2011 2012 2013 2014

Year 0 1 2 3 4

Market Re 26000 26520 27050.4 27591.41 28143.24

Rental Income (calendar years)

Unit 1 21800 26520 26520 26520

Unit 2 26000 26000 26000 26000

Unit 3 25070 25070 25070 25070

Total 72870 77590 77590 77590

Capital ###

LeaseStart

LeaseEnd

Rent

ReviewFrequency

NextRentReview

RentPassing000


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Net Cash ### 72870 77590 77590 77590

PV of 1 1 0.93 0.87 0.8 0.75

PV of Cas ### 67786.05 67141.16 62456.89 58099.43

Net Prese 0 sum of PV of Cash FlowNet Prese 0 formula = NPV(Required Return,Future


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e cash flow is rental income. (There are others, such as landlords' costs we will ignore her

day, set at the start of the lease or last rent review.

t Rental Value): the rent the building wouldtal Value varies with the demand and supply -

d current rate of development completions.

iodically through the lease. In the UK, usually an Upward Only Rent Review -

lue only if Market Rental Value is higher than Rent Passing - every 5 years.

tenant which runs for a specified term, in the UK usually from 5 to 15 years.

ture income from investments will be something like this. For simplicity all dates are at th

26000

26000

26000

y, and decide how much we might bid to buy it.

pa

d, and the income from each unit (rent reviews are indicated in yellow)

urchase price of 1m (shown as a negative cashflow in year 0)

flows and by using the Excel NPV function

the initial purchase price which sets the NPV to zero

2015

5

28706.1Rental value with compound growth @ 2%

26520Rental income raised to market rental value after each review date (in yellow)

26000

28143.24

80663.24Sum of unit rental incomes

1400000Assume sale at 1.4 million, purchase at end 2010 at -GUESS

Market

RentalValue000


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###Sum of Income & Capital

0.7 formula 1 / (1 + Required Return)^Year Number

###Net Cash Flow x PV of 1

ash Flows) + Year 0 Cash Flow


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.)

year end


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Basic ChartsCharts are often (though not always) a useful way of summarising complex dat

The Insert Ribbon shows the basic Excel Charts; click the little arrow in the bott

There are two main ways of creating an Excel chart:

- highlight the blocks of data you want to chart, select Insert and then

- highlight the blocks of data you want to chart, hit F11, Excel creates

It is easiest to have all the data you need in a single block. To use separate blo

Unfortunately the default formatting of charts created by Excel is fairly nasty. F

Basically you change anything in a chart by selecting types & layouts from the

Use the data below to create nice looking, properly titles and labelled,

- a line plot comparing annual total returns across all countrie

- a line plot comparing the Indices of total returns across all c

- a column (or bar) chart comparing average returns across co

- a scatterplot comparing returns and risks over the whole per

Experiment with putting charts onto the current sheet, or creating the

All Property Total Returns % pa

Australia Canada France UK USA

1990 -0.4 4.3 15.3 -8.4 2.3 19901991 -9.2 0.2 6.7 -3.1 -5.6 1991

1992 -5.5 -5.5 2.8 -1.6 -4.3 1992

1993 1.5 -6.4 -2.0 20.2 1.4 1993

1994 12.3 1.9 -2.4 11.9 6.4 1994

1995 8.3 5.0 -8.0 3.6 7.5 1995

1996 8.4 7.0 -4.5 10.0 10.3 1996

1997 10.7 18.5 0.9 16.8 13.9 1997

1998 10.3 16.0 5.4 11.8 16.2 19981999 9.7 10.6 13.4 14.5 11.7 1999

2000 11.0 11.9 14.2 10.5 12.5 2000

2001 10.7 9.2 9.7 6.8 6.4 2001

2002 9.8 8.8 8.6 9.6 6.1 2002

2003 12.2 8.3 8.0 10.9 9.9 2003

2004 14.0 12.9 10.0 18.3 13.1 2004

2005 15.7 18.7 15.4 19.1 19.2 2005


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2006 19.2 18.3 21.9 18.1 15.0 2006

2007 18.3 15.8 17.8 -3.4 14.3 2007

2008 -0.3 3.7 -0.9 -22.1 -7.4 2008

2009 -2.2 -0.3 -1.4 3.5 -17.1 2009

Source: IPD Source: IP

Average Return

Risk (Std Dev)

Charts for Data Analysis - Scatterplots

Besides making pretty pictures, charts can be useful for visualising data, for ex

For example, a line chart of the data above suggests USA and Australia are stro

but not with France.

Scatterplots are useful for bringing out relationships, and generating some of th

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

-20.0

-10.0

0.0

10.0

20.0

30.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.025.0

Scatterplot Australia vs USA 1990-

ReturnUS

A


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Charts for Data Analysis - Trendlines

Adding trendlines is a handy way of highlighting long run underlying trends, an

Right-Click the series, select Add Trendline. The appropriate form of tr

For example, this chart shows that retail rental values have fallen much further

Indices of Real Rental Values, UK

Retail Office Industrial

1975 100 100 100

1976 93 87 93

1977 88 80 89

1978 91 80 89

1979 90 77 89

1980 89 75 88

1981 87 73 82

1982 87 71 80

1983 87 69 76

1984 89 68 75

1985 92 68 73

1986 98 74 73

1987 109 88 79

1988 122 104 91

-15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0

Return Australia

-10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

Scatterplot France vs USA 1990-20

Return France

ReturnUS

A

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1

20

40

60

80

100

120

140

UK Rea


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1989 129 110 102

1990 123 101 100

1991 115 82 93

1992 109 64 83

1993 104 54 74

1994102 52 70

1995 100 50 66

1996 102 50 66

1997 106 54 66

1998 109 57 68

1999 113 60 69

2000 115 66 71

2001 117 69 72

2002 118 61 72

2003 119 53 70

2004 120 51 68

2005 121 52 68

2006 119 53 66

2007 117 56 64

2008 116 54 64

2009 107 45 59

Source: IPD


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.

m right to see lots.

the chart type you want, Excel inserts a small chart on your current sheet

a big chart on a new sheet, change the type to what you want from the top ribbon.

ks, highlight each range you want you use, then hold down Ctrl and highlight the next.

ortunately you have huge control over colours, font sizes etc etc to make them look nice.

ibbon, or by Right-Clicking any element in the chart to bring up a context menu.

charts showing:

untries

ntries over the whole period, 1990-1999 and 200-2009

iod across countries

m in separate sheets.

All Property Total Returns % pa

Australia Canada France UK USA

100 100 100 100 100


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D

mple looking for relationships.

ngly correlated with each other

e basic statistical results.

Once you have created the scatterplot

- right click on the data points and select Add Trendline

You can see straightaway the strength of the association.

- check the boxes for in Display Equation and Display R2

The R2 = square root of the correlation between the series

2009

Australia

France

USA


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While the one for France looks much weaker.

how far the variable is from trend.

endline depends on the nature of the data.

against long run trends than other sectors.

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

Documents

MSC Induction 2010 - Intermediate Excel Exercises