Chapter 13: return, risk, and the security market line
13.1 Expected returns and variances
Expected return
Ex:
● consider a single period of time, one year. We have 2 stocks, L and U
● Stock L is expected to have a return of 25% in the coming year
● Stock U is expected to have a return of 20% for the same period
● If all investors agreed on the expected returns, why would anyone want to hold Stock U?
● Why invest in one stock when the expectation is that another will do better?
○ Depends on the risks of the two investments
● Suppose the economy booms, Stock L will have a 70% return, if economy enters a recession, the
return will be -20%
● These are the 2 states of the economy, the only two possible situation's (boom and recession)
● What you earn in any particular year depends on what the economy does during that year
● Suppose we think a boom and a recession are equally likely to happen (50-50 chance)
● For Stock U, if recession, earns 30%, if boom, earns 10%
● Suppose the probabilities stay the same through time
○ If you hold Stock U for a # of years, you will earn 30% half the time and 10% the other
half
○ Your expected return on Stock U, E(RU) is 20%:
E(Ru) = 0.5 x 30% + 0.5 x 10% = 20%
● On average, you should expect to earn 20% form this stock
● For Stock L, the probabilities are the same, but the possible returns are different
○ Would lose 20% half the time and gain 70% the other half
○ Your expected return on Stock L, E(RL) is 25%:
E(RL) = 0.5 x -20% + 0.5 x 70% = 25%
1
, ● Risk premium is the difference between the return on a risky investment and that on a risk-free
investment (risky investment vs. risk-free investment)
Risk premium = Expected return - risk-free rate
E(RM) - Rf
● Projected/expected risk premium is the difference between the expected return on a risky
investment and the certain return on a risk-free investment (expected return in risky investment
vs. expected return in risk-free investment)
Ex: suppose risk free investments are currently offering 8% --> risk-free rate (Rf) is 8%
● The projected risk premium on Stock U:
○ Expected return on Stock U, E(RU) = 20%
Projected risk premium = expected return - risk-free rate
= E(RU) - Rf
= 20% - 8%
= 12%
● Projected risk premium on Stock L:
Projected risk premium = expected return - risk-free rate
= E(RL) - Rf
= 25% - 8%
= 17%
● The expected return on a security or other asset is equal to the sum of the possible returns
multiplied by their probabilities (possible return x probabilities)
● The risk premium would be the difference between this expected return and the risk-free rate
Ex 2:
● Suppose you think a boom will occur only 20% of the time instead of 50%. What are the
expected returns on Stock U and L in this case? If the risk-free rate is 10%, what are the risk
premiums?
Expected return:
2
13.1 Expected returns and variances
Expected return
Ex:
● consider a single period of time, one year. We have 2 stocks, L and U
● Stock L is expected to have a return of 25% in the coming year
● Stock U is expected to have a return of 20% for the same period
● If all investors agreed on the expected returns, why would anyone want to hold Stock U?
● Why invest in one stock when the expectation is that another will do better?
○ Depends on the risks of the two investments
● Suppose the economy booms, Stock L will have a 70% return, if economy enters a recession, the
return will be -20%
● These are the 2 states of the economy, the only two possible situation's (boom and recession)
● What you earn in any particular year depends on what the economy does during that year
● Suppose we think a boom and a recession are equally likely to happen (50-50 chance)
● For Stock U, if recession, earns 30%, if boom, earns 10%
● Suppose the probabilities stay the same through time
○ If you hold Stock U for a # of years, you will earn 30% half the time and 10% the other
half
○ Your expected return on Stock U, E(RU) is 20%:
E(Ru) = 0.5 x 30% + 0.5 x 10% = 20%
● On average, you should expect to earn 20% form this stock
● For Stock L, the probabilities are the same, but the possible returns are different
○ Would lose 20% half the time and gain 70% the other half
○ Your expected return on Stock L, E(RL) is 25%:
E(RL) = 0.5 x -20% + 0.5 x 70% = 25%
1
, ● Risk premium is the difference between the return on a risky investment and that on a risk-free
investment (risky investment vs. risk-free investment)
Risk premium = Expected return - risk-free rate
E(RM) - Rf
● Projected/expected risk premium is the difference between the expected return on a risky
investment and the certain return on a risk-free investment (expected return in risky investment
vs. expected return in risk-free investment)
Ex: suppose risk free investments are currently offering 8% --> risk-free rate (Rf) is 8%
● The projected risk premium on Stock U:
○ Expected return on Stock U, E(RU) = 20%
Projected risk premium = expected return - risk-free rate
= E(RU) - Rf
= 20% - 8%
= 12%
● Projected risk premium on Stock L:
Projected risk premium = expected return - risk-free rate
= E(RL) - Rf
= 25% - 8%
= 17%
● The expected return on a security or other asset is equal to the sum of the possible returns
multiplied by their probabilities (possible return x probabilities)
● The risk premium would be the difference between this expected return and the risk-free rate
Ex 2:
● Suppose you think a boom will occur only 20% of the time instead of 50%. What are the
expected returns on Stock U and L in this case? If the risk-free rate is 10%, what are the risk
premiums?
Expected return:
2
