finance
Class Notes – Ch 7 Risk, Reward and the CAPM
Rational investors expect returns as a reward for taking risk. Returns are usually expressed as a performance number- either as a $ return or as a percentage.
Therefore we need to be able to measure the level of risk inherent in a potential investment, and we also need to be able to calculate the expected return for that risk.
Risk is not achieving the return that is expected
We measure risk by calculating variance and standard deviation – these show the volatility of the returns – the higher the volatility the higher the uncertainty, the higher the risk.
Look at the chart on p231 – showing the probability distribution of two companies’ expected rates of return. Probability shows the chance that the event will occur, so the chart shows the possible returns that could occur from holding the two stocks. One has a very wide distribution of probabilities – therefore more volatile results so higher risk. The other stock has a much narrower range of possible returns therefore is lower risk.
Standard deviation
Historical variance is the sum of the squared deviations from a mean divided by the number of observations minus one. SD is the positive square root of that variance. This is the level of risk. The higher the number, the higher the level of risk.State of economy Probability of state Return on A Return on B
Boom .40 30% -5%
Bust .60 -10% 25%
100% Expected return
E(RA) = .4(.30) + .6(-.10) = .06 = 6%
E(RB) = .4(-.10) + .6 (.25) = .13 = 13%
Variance
Var A = .4(.30-.06)^2 + .6(-.10-.06)^2 = .0384
Var B = .4(-.05-.13)^2 + .6(.25-.13)^2 = .0216
SD A = 19.6%
SD B = 14.7%
The above shows the expected return and risk of holding an individual stock – either A or B
But we would like to maximize our investment returns while having the lowest level of risk.
Look at a portfolio of the two stocks with 50% held in each:
State of economy Probability of state A B Return on portfolio
Boom .40 30% -5%
Rational investors expect returns as a reward for taking risk. Returns are usually expressed as a performance number- either as a $ return or as a percentage.
Therefore we need to be able to measure the level of risk inherent in a potential investment, and we also need to be able to calculate the expected return for that risk.
Risk is not achieving the return that is expected
We measure risk by calculating variance and standard deviation – these show the volatility of the returns – the higher the volatility the higher the uncertainty, the higher the risk.
Look at the chart on p231 – showing the probability distribution of two companies’ expected rates of return. Probability shows the chance that the event will occur, so the chart shows the possible returns that could occur from holding the two stocks. One has a very wide distribution of probabilities – therefore more volatile results so higher risk. The other stock has a much narrower range of possible returns therefore is lower risk.
Standard deviation
Historical variance is the sum of the squared deviations from a mean divided by the number of observations minus one. SD is the positive square root of that variance. This is the level of risk. The higher the number, the higher the level of risk.State of economy Probability of state Return on A Return on B
Boom .40 30% -5%
Bust .60 -10% 25%
100% Expected return
E(RA) = .4(.30) + .6(-.10) = .06 = 6%
E(RB) = .4(-.10) + .6 (.25) = .13 = 13%
Variance
Var A = .4(.30-.06)^2 + .6(-.10-.06)^2 = .0384
Var B = .4(-.05-.13)^2 + .6(.25-.13)^2 = .0216
SD A = 19.6%
SD B = 14.7%
The above shows the expected return and risk of holding an individual stock – either A or B
But we would like to maximize our investment returns while having the lowest level of risk.
Look at a portfolio of the two stocks with 50% held in each:
State of economy Probability of state A B Return on portfolio
Boom .40 30% -5%