Personal Financial Management

Semester 2 2008 – 2009

Gareth Myles g.d.myles@ex.ac.uk

Paul Collier p.a.collier@ex.ac.uk

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