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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 5 McRae: Chapter 2. Risk and Return. Consider two work colleagues who share a £200,000 lottery win early in 1994
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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 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
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
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
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
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 Return Mean Return Period
Risk Return • Considerable risk Mean Return Period
General Motors 25 years
General Motors 6 months
General Motors 5 days
General Motors 1 day
General Motors 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:
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
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: • 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:
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 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 • 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