FINS2624 Chapter Notes - Chapter 6-8: Risk Premium, Risk Aversion, Indifference Curve

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16 May 2018

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Chapter 6

- Speculation is the undertaking of a risky investment for its risk premium. The risk

premium has to be large enough to compensate a risk-averse investor for the risk of

the investment.

- A fair game is a risky prospect that has a zero risk premium. It will not be undertaken

by a risk-averse investor

- Iestors’ preferees toard the epeted retur ad olatilit of a portfolio a

be expressed by a utility function that is higher for higher expected returns and

lower for higher portfolio variances. More risk-averse investors will apply greater

penalties for risk. We can describe these preferences graphically using indifference

curves.

- The desirability of a risky portfolio. The certainty equivalent rate of return is a value

that, if it is received with certainty, would yield the same utility as the risky portfolio

- Shifting funds from the risky portfolio to the risk-free asset is the simplest way to

reduce risk. Other methods involve diversification of the risky portfolio and hedging

- An investor’s risk portfolio risk asset a e haraterised  its reard-to-

volatility, S = (E(rP) – rf)/ σP . This ratio is also the slope of the CAL, a line that goes

from the risk free asset through the risky asset. Other things equal, an investor

would prefer a steeper-sloping CAL, because that means higher expected return for

any level of risk. If the borrowing rate is greater than the lending rate, the CAL will be

kinked at the point of the risky asset

- The investors degree of risk aversion is characterised by the slope of their

indifference curve. Indifference curves show, at any level of expected return and

risk, the required risk premium for taking on one additional percentage point of

standard deviation. More risk-averse investors have steeper indifference curves-

require greater risk premium for taking on more risk

- Optimal position y* in risky asset is proportional to risk premium and inversely

proportional to variance and degree of risk aversion: y* = (E(rP) – rf/A*σP2 → point

at which indifference curve is tangent to CAL

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Document Summary

Speculation is the undertaking of a risky investment for its risk premium. The risk premium has to be large enough to compensate a risk-averse investor for the risk of the investment. A fair game is a risky prospect that has a zero risk premium. It will not be undertaken by a risk-averse investor. I(cid:374)(cid:448)estors" prefere(cid:374)(cid:272)es to(cid:449)ard the e(cid:454)pe(cid:272)ted retur(cid:374) a(cid:374)d (cid:448)olatilit(cid:455) of a portfolio (cid:373)a(cid:455) be expressed by a utility function that is higher for higher expected returns and lower for higher portfolio variances. More risk-averse investors will apply greater penalties for risk. We can describe these preferences graphically using indifference curves. The certainty equivalent rate of return is a value that, if it is received with certainty, would yield the same utility as the risky portfolio. Shifting funds from the risky portfolio to the risk-free asset is the simplest way to reduce risk. Other methods involve diversification of the risky portfolio and hedging.

Related Questions

Consider a risky portfolio that offers a rate of return of 15% per year with a standard deviation of 20% per year. Suppose an investor is indifferent between investing in the risky portfolio and investing in a risk free asset earning 8% per year.
a) What is the investor's risk aversion coefficient?
b) If allowed to invest in a combination of the risky portfolio and the risk free asset, what proportion would the investor hold in the risky portfolio?
c) What is the expected rate of return and the standard deviation of the rate of return on the optimally chosen combination?
d) What would be the investor's certainty equivalent return for the optimally chosen combination?

Evaluating risk and return

Stock X has a 9.5% expected return, a beta coefficient of 0.8, and a 40% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.

Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations.
CVx =
CVy =

Which stock is riskier for a diversified investor?

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X.

For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the higher standard deviation of expected returns is more risky. Stock X has the higher standard deviation so it is more risky than Stock Y.

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the lower beta is more risky. Stock X has the lower beta so it is more risky than Stock Y.

For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the lower standard deviation of expected returns is more risky. Stock Y has the lower standard deviation so it is more risky than Stock X.

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is less risky. Stock Y has the higher beta so it is less risky than Stock X.

-Select-IIIIIIIVVItem 3

Calculate each stock's required rate of return. Round your answers to two decimal places.
rx = %
ry = %

On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor?
-Select-Stock XStock YItem 6

Calculate the required return of a portfolio that has $4,500 invested in Stock X and $9,000 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places.
rp = %

If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?
-Select-Stock XStock Y

Evaluating risk and return

Stock X has a 10.0% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.0% expected return, a beta coefficient of 1.1, and a 30.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.

Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations.
CVx =
CVy =

Which stock is riskier for a diversified investor?

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X.

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the lower beta is more risky. Stock X has the lower beta so it is more risky than Stock Y.

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is less risky. Stock Y has the higher beta so it is less risky than Stock X.

-Select-IIIIIIIVVItem 3

Calculate each stock's required rate of return. Round your answers to two decimal places.
rx = %
ry = %

On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor?
-Select-Stock XStock YItem 6

Calculate the required return of a portfolio that has $10,000 invested in Stock X and $5,000 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places.
rp = %

If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?
-Select-Stock X or Stock Y?

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FINS2624 Chapter Notes - Chapter 6-8: Risk Premium, Risk Aversion, Indifference Curve

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