Personal Financial Management Semester – 2009 Gareth Myles Paul Collier

Reading Callaghan:Chapter 5 McRae: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

Entire Period For the story of the Marconi collapse, see: End of the Line for Marconi Shares

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 Return is defined over a fixed time period, usually 1 year but can be 1 month etc. It can be applied to any asset

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 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 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 Return

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 Not much risk Period Return Mean Return

–Considerable risk Period Return Mean Return Risk

General Motors 25 years

General Motors 6 months

General Motors 5 days

General Motors 1 day

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” equally Should be measured relative to average value:

Measurement of Risk Example. A share is observed for 5 years. In these years it earns returns of 2%, 6%, 3%, 8% and 1%.

Variance and Standard Deviation The risk is defined as the variance of return Or, in brief

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: 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: Variance and Standard Deviation

Standard Deviation The risk can also be measured by the standard deviation This is the square root of the variance The two are equivalent

Return and Risk Table taken from: Risk and ReturnRisk 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 government- backed) have the lowest return Risk-free assets 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