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Personal Financial
Management
Semester 2 2008 – 2009
Gareth Myles [email protected]
Paul Collier [email protected]
Reading
Callaghan:
 McRae:

Chapter 5
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
350000
300000
250000
200000
Marconi
150000
Deposit
100000
50000
0
1
2
3
4
5
6
7
8
Entire Period
350000
300000
250000
200000
Marconi
150000
Deposit
100000
50000
0
1
2
3
4
5
6
7
8
9
For the story of the Marconi collapse, see:
End of the Line for Marconi Shares
10
11
Lessons?
Different investments, different outcomes
 Some are safe (deposit account), some
are not (shares)
 Trends cannot be forecast
 Should 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
Final Value - Initial Value
Return (%) 
(100)
Initial 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
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:
1050 - 1000
Return 
 100  5%
1000
So the return can also be viewed as an
interest rate
Return

Example 2. A share is bought for £4.
One year later it is sold for £5
5-4
Return 
 100  25%
4

Example 3. A share is bought for £4 One
year later it pays a dividend of £1 and is
then sold for £5
5 1- 4
Return 
 100  50%
4
Return
• Example 4. A share is bought for £12. One
year later it is sold for £10.
10 - 12
2
Return 
 100  16 %
12
3
- The return can be negative
• The definition of return can be applied to
any asset or collection of assets
• Classic Cars
• Art
Expected Return

The previous calculations have been
applied to past outcomes


Can call this “realized return”
When choosing an investment expected
return is important
Expected return is what is promised
 Realized return is what was delivered

Expected Return

Expected return is calculated by
Evaluating the possible returns
 Assigning a probability to each
 Calculating the expected value


Example 1
Toss a coin
 Receive £1 on heads, £2 on tails
 Expected value is (1/2) 1 + (1/2) 2 = 1 1/2

Expected Return

Example 2
Buy a share
 Return 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
Return
Mean
Return

Not much risk
Period
Risk
Return
Mean
Return
– Considerable risk
Period
General Motors
25 years
General Motors
6 months
General Motors
5 days
General Motors
1 day
General Motors
40
30
20
10
0
-10
-20
93- 94- 95- 96- 97- 98- 99- 00- 01- 0294 95 96 97 98 99 00 01 02 03
-30
-40
-50
Return on General Motors’ Shares 1993 – 2003
Measurement of Risk
Need a number that is always positive
(the least risk is zero)
 Must treat “ups” and “downs” equally
 Should be measured relative to average
value:

Sum of Observed Returns
Mean Return   
Number of Observations
Measurement of Risk

Example. A share is observed for 5
years. In these years it earns returns of
2%, 6%, 3%, 8% and 1%.
2  6  3  8 1
Mean Return   
4
5
Variance and Standard Deviation

The risk is defined as the variance of
return
Sum of (Observation - Mean)
Variance   
Number of Observations
2

Or, in brief
n
 ri   
  i 1
2
2
n
2
Variance and Standard Deviation
Example 1. The returns on a share over
the past five years are 5, 8, 4, -2, 1. The
mean return is:
5  8  4  3 1

3
5
 And the variance is:


2

5  3  8  3  4  3   3  3  1  3

2
2
2
5
4
 10
5
2
2
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:
7  10  6  6  2

3
5

And the variance is:
2
2
2
2
2










7

3

10

3

6

3


6

3


2

3
2 
5
 36
Standard Deviation

The risk can also be measured by the
standard deviation

This is the square root of the variance
Standard devation  Square Root of Variance
  2

The two are equivalent
Return and Risk
Asset
1-Mo T-bills
Annualized
Return (%)
1926 - 98
3.77
SD (%) Worst return for
1926 - a single year
98
(%) 1926 - 98
3.22
0.00
5-Yr Treas.
5.31
5.71
-2.65
20-Yr Treas.
5.34
9.21
-9.8
Large Stocks 11.22
20.26
-43.3
Small Stocks 12.18
38.09
-58.0
Table taken from: Risk and Return
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 investment
Risk-free assets (meaning governmentbacked) have the lowest return
 Risky 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 involved
 Marconi shares offered a higher return than
the deposit account but the collapse was
the “risk”


This should always be remembered

an investment is judged on its combination
of return and risk