Introduction to Investment Analysis_rates_of_return

8/7/2019 Introduction to Investment Analysis_rates_of_return

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Introduction to Investment

Analysis

Rates of Return


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Investment Return

Investment Horizon or Holding Period is the

period between the purchase and sale date.

How do you know how well an investment hasdone?

Ans. You calculate the rate of return

Historical rates of return are used to develop an

estimate of the expected rate of reurn


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Components of Investment Return

1. Current Income is the periodic income that aninvestment generates.

a) Interest for bondsb) Dividends for stocks

c) Rent for real estate

To be considered income, it must be received in

the form of cash or be readily convertible intocash

2. Capital Gains (Loss) = appreciation or

increase (Decrease) in value of the investment.


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Total Return

Total return in Dirham =Current Income +

Capital Gains

Never compare two investments based on the

total return in Dirhams. Instead use the rate

of return

InvestmentInitialturnTotalr

Re!


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Holding Period Return

V1= The market value of the portfolio at the end of the interval.

V0= The market value of the portfolio at the begging of the interval

Cash Flow = cash distribution to the investor

Dividends in the case of Stocks

Interest in the case of Bonds

Rent in the case of Real Estate

0

01)(

V

VVFlowCashR

p

!


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Investment Return

0

)01

(

0

)(

0

01

V

VV

V

loas

p

V

VVloasp

!

!


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Investment Return

HPR =

Dividend Yield + Capital Gains Yield

in the case of Stocks

Current Yield + Capital Gains Yieldin the case of bonds


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Holding Period Returns

Can be calculated for any investment horizon

We can calculate six-month holding period return

or a one year holding period return

However, we can only compare holding period

returns for similar holding periods.

A one year HPR can only be compared with one

year HPR. A six-month HPR can only be

compared with a six-month HPR.


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Understanding Return Components

Current income is realized return because theinvestor generally receives current income during

the period.

Capital gains (losses) may or may not be realized.

Capital gains (losses) are realized only if theinvestment is sold at the end of the holding period.

If the investment is not sold at the end of the holdingperiod, then any gains(losses) are unrealizedgains(losses) also called paper gains (losses).


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Understanding Return Components

Both current income and capital gains may be

negative.

Any investment in Stocks, Bonds, or Real Estatemay result in capital loss.

But how would a current income be negative?

An investor may have to pay out more than he

receives from an investment. Occurs mostly with real

estate investments when the rent is less than the

associated payments of maintenance, for example.


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How to compare investments

with different time horizons? We bring both investments to a common

denominator. The best way is to annualize

the returns.

Mistake at the bottom of page 9 and top of

page 10.

periodoldi gaiyearsofmbert eisere

HPAHP

""

1)1(1

!


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Calculate the Mean historical rates of return

A security may have achieved different

rates of return over a number of years.

We need a summary measure that would

indicate the investments typical

performance.

Two summary measures are available

Arithmetic Mean and Geometric Mean


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Arithmetic Mean

The Formula for the Arithmetic Mean is:

The Formula for the Geometric Mean is,

The Geometric Mean measures the compoundrate of growth of the initial portfolio during theperiod.

n

HP

Mean

Arit metic

7!

1)1(1

! nHPMeanGeometric prod ctmeans


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Comparison of the Geometric

and the Arithmetic Mean The Arithmetic mean Geometric mean

The only time they are equal is when the returns

are identical. When do we use each method?

Use the geometric mean when

Use the geometric average if you are concerned with long-termperformance, as are a lot of investors. It is the better measure ofreturn because it measures the compound measure of return.

When we wish to estimate the ending value of an investment overa multi-period horizon conditioned on past experience. i.e., toestimate the future value based on past experience.

u


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Comparison of the Geometric

and the Arithmetic Mean The Arithmetic mean provides a good indication

of what would be the next years expected rate of

return. It is our best guess of the HPR in a givenyear.

It overestimates the assets long-run

performance.

The difference between the arithmetic and the

geometric rates will increase as the variability of

the holding period returns increases.


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Risk and Return

Realized return is the return that was earned.

Expected return is an estimated return that

investors anticipate over some period. It is subjectto uncertainty and may not occur.

Investors like to maximize expected returns subjectto some constraints. Risk is the primary constraint.

People dont make their decisions based only onreturn. They need to take risk into consideration.

Risk is the chance that the actual return of aninvestment will differ from the expected outcome.


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Risk and Return

Risk is associated with the dispersion in

the likely outcomes. If an asset has no

variability, it has no risk.

The most common form of dispersion is

the standard deviation of return. The

higher the value of the standard deviation,the more dispersion and the riskier the

investment is.


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Required rate of return

When selecting securities we have to find onethat provides a rate of return that compensates us

for three things: The Time Value of Money The expected rate of inflation

The risk involved

Also called the discount rate.

It is the rate that the investors require if theinvestor is to invest in a particular security.


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Required rate of return

The required rate of return

The real risk free rate is the basic interest rate, assumingno inflation and no uncertainty about future cash flows.The only sacrifice was deferring using the money for a

period of time.

An investor in an inflation-free economy who knew withcertainty what cash flows he/she would receive at whattime would demand the real-risk free rate on an

investment. The only sacrifice was deferring using themoney for a period of time, i.e., deferring consumption.

pemi mInflationrateFreeiskalralNo

emi miskemi mInflationratefreeriskalr

f!

!

Remin

PrPrRe


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What influences the risk free rate?

Q: What influences people to postponeconsumption. This depends on:1. Time preference of individuals. Since this varies for investors, the

market creates a composite rate that includes the preference of allinvestors.

This composite changes over time but it is a gradual change sinceall investors in the economy influence it.

The changes in consumption preferences might be offset by thechanges in different set of investors

2. The set of investment opportunities available in the economy and isdetermined by the long-run real growth rate in the economy.

A rapidly growing economy has more investment opportunities toinvest the funds and experience positive rates of return.

Those looking to invest in a rapidly growing economy would

require a higher rate of return and those looking for funds areready to pay a higher rate because of the growth.


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Investing contains risk

Required rate of return will be composed of twoelements:

1. A real risk free rate2. A risk premium to compensate for the added risk

taken

Purchasing any security (financial instrument)has risk.

Investors are risk-averse. They are not willingto take on more risk unless they arecompensated with extra return. The higher therisk of the security the higher will be the

required rate of return.


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Purchasing Power Risk (Inflation Risk)

As an investor you would like to get back yourmoney plus some form of current income and/orcapital gains.

If your HPR over a seven-year period was 80%,are you better off??

The answer really depends on inflation (level ofprices) experienced over the same period. If

inflation went up by 100%, then clearly you areworse off.

You are worse off because the investor is clearlyreceiving an amount that is lesser in value than the

one originally invested.


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Inflation reduces the purchasing

power of investment returns If a bank advertises 7% on its savings account,

the advertised amount is the nominal rate of

return; they are not adjusted for inflation. You are better off in purchasing power terms if

the nominal return is more than the inflation rate.

If your return over a year, 15% when the rate of

inflation over the same period was 10%, the

portfolios real rate of return is approximately

rateInflationratealNoret r nofrateal ! minRe


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Real rate of return

Real rate of return = 15%-10%=5%

The investor is better off by 5% in real

terms (purchasing power terms).

From the 15% gain, 10% has been lost to

inflation. 5% results in real gain, which is

increased consumption.

The exact real rate of return formula is:

1

inf1

min1Re

!

ratelation

ratealNoreturnrateal


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Real Rate of return

If an investors portfolio had a return of 8% whenthe rate of inflation was 10%, then the rate of

return is approximately2%. The only sacrificewas deferring using the money for a period oftime.

Q: Would our investor have been better offwithout that investment; that is left his money incash?

A: Clearly No. Had our investor left his moneyin cash, the nominal rate = 0 and the real ratewould have been 0% -10% = -10% which is way

worse that 2%.


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Inflation and Stock Returns

Over the long run investors enjoyed real rates ofreturn on common stock. However, over shorter

periods, inflation can and did exceed the nominalrates thus producing negative rates of return anddisappointed investors who regarded equities as ahedge against inflation.

As t e i nvestment orizon is increased, ret rnson common stocks o tpaced inflation over moreperiods and to a greater degree t an t e ot er assets and ere more volatile t an any of t em.


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Effects of Inflation

Assume the historical inflation rate =

3.1%.The value of one Dirham in:

417.0)0301.01(130

5526.0)0301.01(120

74337.0)0301.01(110

30

20

10

AEDAEDyears

AEDAEDyears

AEDAEDyears

!!

!!

!!


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Effects of Inflation

Inflation can relegate

even the mostconservative

investments in tospeculative status.

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Introduction to Investment Analysis_rates_of_return