MFIN1021 Chapter Notes - Chapter 12: Risk Premium, Market Risk, Expected Return

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11 Jun 2018

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Chapter 12

Definitions:

Market Portfolio: Portfolio of all assets in the economy in practice a board stock market

index is used to represent the market

Beta: sensitivity of a stock’s return of return on the market portfolio

Market risk Premium: risk premium of market portfolio. Difference between market return

and return on risk-free treasury bills.

CAPM(Capital assets pricing model): Theory of the relationship between risk and return

which states that the expected risk premium on any security equal it’s times the market

risk premium.

Security market line: relationship between expected return and beta

Project cost of capital: minimum acceptable expected rate of return on a project given its

risk

Company cost of capital: Opportunity cost of capital for investment in the firm as a whole.

The company cost of capital is the appropriate discount rate for an average-risk

investment project undertaken by the firm.

Formal’s :

Portfolio beta: = (faction of 1 stock in portfolio * beta ) + (fraction of 2 stock in portfolio *

beta)…

Market risk Premium: Risk of Market- risk free t-bill rate

Risk Premium: B*( Rm- Rf)

Expected return of rate: Rf+ B*(Rm- Rf)

Rules:

1. Aggressive stocks have high betas, betas greater than 1.0. Their returns tend to

respond more than one for one to returns on the overall market. The betas of defensive

stocks are less than 1.0. The returns of these stocks vary less than one for one with market

returns. The average beta of all stocks is—no surprises here—1.0 exactly.

2. As this example illustrates, we can break down common stock returns into two parts:

the part explained by market returns and the firm’s beta, and the part due to news that is

specific to the firm. Fluctuations in the first part reflect market risk; fluctuations in the

second part reflect specific risk.

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Document Summary

Market portfolio: portfolio of all assets in the economy in practice a board stock market index is used to represent the market. Beta: sensitivity of a stock"s return of return on the market portfolio. Market risk premium: risk premium of market portfolio. Difference between market return and return on risk-free treasury bills. Capm(capital assets pricing model): theory of the relationship between risk and return which states that the expected risk premium on any security equal it"s times the market risk premium. Security market line: relationship between expected return and beta. Project cost of capital: minimum acceptable expected rate of return on a project given its risk. Company cost of capital: opportunity cost of capital for investment in the firm as a whole. The company cost of capital is the appropriate discount rate for an average-risk investment project undertaken by the firm.

Related Questions

Calculating the market risk premium beta and required rate of return. CAPM. Portfolio Risk & Return.

We have a portfolio of three positively correlated but not perfectly correlated stocks.

(Correlation co-efficient between 0-1)

Stock Expected Rate of Return Standard Deviation Beta

X 10% 16% .75

Y 12% 16% 1.25

Z 13% 16% 1.50

What is the market risk premium for the portfolio ?

Required Rate of Return For the Stock = Risk Free rate of Return +

+ ( Market Risk Premium * Beta of stock )

Market Risk Premium = Market Required Rate of Return â Risk Free rate of Return

The returns on stocks X, Y and Z and their beta have been provided. Using the information provided, we will first calculate the market risk premium.

The capital asset pricing model is a model based on the proposition that any stock's required rate of return is equal to the risk free rate of return plus a risk premium that reflects only the risk remaining after diversification.

The required rate of return for a stock is calculated by adding the risk free rate of return to the product of the market risk premium and the stock's beta.

The market risk premium shows the premium that investors require for bearing the risk of average stock and is calculated by deducting the risk free rate from the market's required rate of return.

Now, using stock X or any other stock, we can calculate the market risk premium. We'll use stock X. The expected return on this stock is 10%. The risk free rate is 7& and the stock's beta is .75.

By solving the equation we determine the market risk premium to be 4%.

Next, we will calculate the beta of Fund Q.

Fund Q has 1/3 of its funds invested in each of the three stocks X, Y, and Z.

Thus, the beta of Fund Q will be the sum of one third of the beta of each stock. One third of .75 is .25. One third of 1.25 is .4167 and one third of 1.5 is .5. By adding .25, .4167 and .5, we calculate the beta of Fund Q as 1.1667.

Letâs now calculate the required return of Fund Q. The risk free rate is 7%. The market risk premium is calculated to be 4%. The beta of Fund Q is 1.1667. By adding 7% to the product of 4% and 1.1667, we determine the required return on Fund Q to be 11.67%.

Since the returns on the three stocks included in Fund Q are not positively correlated, the standard deviation of the fund will be less than 16%.

What are the betas listed for these companies?

Wells Fargo beta = 1.03

IBM beta = 0.87

1. If you made an equal dollar investment in each stocks what would be the beta of your portfolio?

2. If you made 70% of dollar investment in stock A, and 30% of dollar investment in stock B, what would be the beta of your portfolio? Please show your work.

3. Apply the Capital Asset Pricing Model (CAPM) Security Market Line to estimate the required return on these two stocks. Assumptions and Data: Note that you will need the risk-free rate and the market risk premium. Assume a 5% market risk premium. You will use the current 2.21 yield on 10-year Treasury securities as the risk-free rate to estimate the required rate of return on stocks.

4. Compare the required return on these stocks calculated using CAPM in question #3 against their historical return over the last 52 weeks (Wells Fargo 59.99) and IBM (182.79). Is there a difference between these returns? Is this a problem? Why is there a difference?

olivewater-buffalo586

Market portfolio has an expected return of 11% and volatility of 20%. Risk-free rate is 3%. Security X and Y have betas of 1.4 and 0.9 respectively.

a) According to CAPM, what are the expected return of X and Y?

E(rm)-rf = 11% - 3% = 8%

3% +1.4*8% = 14.2%

3% +1.4 *8% = 10.2%

b) What should be X worth today, if X pays a dividend of $1.2 one year from today and is priced at 30 one year from today? The required rate of return is the expected return using CAPM from part a).

c) If security X has expected return of 15%, is it underprice/overprice/fairly priced according to CAPM? What is its alpha?

d) Plot SML and label X, Y and Market portfolio on the line.

e) What is the beta of a portfolio with 50% in X and 50% in Y?

f)What is the beta of a portfolio with 55% in Market portfolio and 45% in risk-free asset?

g) You are investing in a complete portfolio. The complete portfolio is composed of risk-free asset and a risky portfolio, P, constructed with 20% in X and 80% in Y. It turns out that your complete portfolio has an expected rate of return of 9.4%. What is the beta of your complete portfolio? (hint: you may or may not use all information to solve this problem)

Q2. Stock A has a beta of 1 and standard deviation of 50%. Market portfolio has a standard deviation of 20%. What is the correlation of stock A with the market portfolio? How much of stock Aâs total risk is due to market risk?

Q3. Assume the risk-free rate is 8% and the expected rate of return on the market is 18%. A stock has an expected return of 6%. What is its beta?

MFIN1021 Chapter Notes - Chapter 12: Risk Premium, Market Risk, Expected Return

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