Embed Size (px)
Citation preview
Personal Financial Management
Semester 2 2008 – 2009
Gareth Myles [email protected]
Paul Collier [email protected]
Reading
Callaghan: Chapter 5McRae: Chapter 2
Risk and Return
Consider two work colleagues who share a £200,000 lottery win early in 1994
Each receives a total of £100,000 Each invests this sum What is their financial position ten years later?
Investment Choices
Investor 1 Studies the financial press Takes note of the share tips Chooses Marconi as a “hot tip”
Investor 2 No time for studying investment Puts all money in a 90-day deposit account
Investment Value up to 2000
0
50000
100000
150000
200000
250000
300000
350000
1 2 3 4 5 6 7 8
Marconi
Deposit
Entire Period
0
50000
100000
150000
200000
250000
300000
350000
1 2 3 4 5 6 7 8 9 10 11
Marconi
Deposit
For the story of the Marconi collapse, see:End of the Line for Marconi Shares
Lessons?
Different investments, different outcomesSome are safe (deposit account), some
are not (shares)Trends cannot be forecastShould diversify (hold a range of assets)
This is portfolio construction
How do we quantify these properties?
Return
The return on an investment is defined as the proportional (or percentage) increase in value
Return is defined over a fixed time period, usually 1 year but can be 1 month etc.
It can be applied to any asset
100)( Value Initial
Value Initial - Value Final (%)Return
Example 1.
£1000 is paid into a savings account. At the end of 1 year, this has risen in value to £1050. The return is:
So the return can also be viewed as an interest rate
%51001000
1000-1050 Return
Return
Example 2. A share is bought for £4. One year later it is sold for £5
Example 3. A share is bought for £4 One year later it pays a dividend of £1 and is then sold for £5
%251004
4-5 Return
%501004
4-15 Return
Return
• Example 4. A share is bought for £12. One year later it is sold for £10.
- The return can be negative
• The definition of return can be applied to any asset or collection of assets
• Classic Cars
• Art
%32
1610012
12-01 Return
Return
Expected Return
The previous calculations have been applied to past outcomesCan call this “realized return”
When choosing an investment expected return is importantExpected return is what is promisedRealized return is what was delivered
Expected Return
Expected return is calculated by Evaluating the possible returnsAssigning a probability to eachCalculating the expected value
Example 1Toss a coinReceive £1 on heads, £2 on tailsExpected value is (1/2) 1 + (1/2) 2 = 1 1/2
Expected Return
Example 2Buy a shareReturn 20% if oil price rises to $70 (prob. =
0.25)Return 5% if oil price remains below $70
(prob. = 0.75)Expected return
(0.25) 20 + (0.75) 5 = 8.75%
Expected Return
Potential investments are compared on the basis of expected return
The use of expected reminds us that nothing is certain
Actual return may be far from the expected value
The mean return (see later) is an estimate of the expected return
Risk
Risk measures the variation in return
Not much risk Period
Return
MeanReturn
– Considerable riskPeriod
Return
MeanReturn
Risk
General Motors
25 years
General Motors
6 months
General Motors
5 days
General Motors
1 day
-50
-40
-30
-20
-10
0
10
20
30
40
93-94
94-95
95-96
96-97
97-98
98-99
99-00
00-01
01-02
02-03
Return on General Motors’ Shares 1993 – 2003
General Motors
Measurement of Risk
Need a number that is always positive (the least risk is zero)
Must treat “ups” and “downs” equallyShould be measured relative to average
value:
nsObservatio ofNumber Returns Observed of Sum
ReturnMean
Measurement of Risk
Example. A share is observed for 5 years. In these years it earns returns of 2%, 6%, 3%, 8% and 1%.
45
18362 ReturnMean
Variance and Standard Deviation
The risk is defined as the variance of return
Or, in brief
nsObservatio ofNumber Mean) -on (Observati of Sum
Variance2
2
n
rn
ii
1
2
2
Example 1. The returns on a share over the past five years are 5, 8, 4, -2, 1. The mean return is:
And the variance is:
35
13485
5
410
5
3133343835 222222
Variance and Standard Deviation
Example 2. The returns on a share over the past five years are 7, 10, 6, -6, -2. The mean return is:
And the variance is:
35
266107
365
32363631037 222222
Variance and Standard Deviation
Standard Deviation
The risk can also be measured by the standard deviationThis is the square root of the variance
The two are equivalent
Variance ofRoot Square devation Standard
2
Return and Risk
Table taken from: Risk and Return
-58.038.0912.18Small Stocks
-43.320.2611.22Large Stocks
-9.89.215.3420-Yr Treas.
-2.655.715.315-Yr Treas.
0.00 3.22 3.77 1-Mo T-bills
Worst return for
a single year (%) 1926 - 98
SD (%)
1926 -98
Annualized
Return (%)
1926 - 98
Asset
-58.038.0912.18Small Stocks
-43.320.2611.22Large Stocks
-9.89.215.3420-Yr Treas.
-2.655.715.315-Yr Treas.
0.00 3.22 3.77 1-Mo T-bills
Worst return for
a single year (%) 1926 - 98
SD (%)
1926 -98
Annualized
Return (%)
1926 - 98
Asset
Market Implications
The market (meaning the average of all investors’ attitudes) Likes returns Dislikes risks
To accept risk, investors must be rewarded with higher return Assets with low risk give low returns Assets with high risk have the possibility of high
return
Market Implications
This relationship will not be violated if it were, trades could be made that gave a
profit for no investmentRisk-free assets (meaning government-
backed) have the lowest returnRisky assets (such as shares) must
promise higher returns
Put Another Way
“There is no such thing as a free lunch” if an asset offers a high return, there must
be a risk involvedMarconi shares offered a higher return than
the deposit account but the collapse was the “risk”
This should always be rememberedan investment is judged on its combination
of return and risk
