# Required Rate of Return, Expected Return, Discrete Distribution

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Please show all the work.

Questions:

1) What types of risk are measured by standard deviation and beta? Which type of risk is more important? Where does correlation fit in? Assume the market risk premium is 5%. Research a current stock and determine its required rate of return using the SML.

#6-3

Security A has an expected return of 7%, a standard deviation of returns of 35%, a correlation coefficient with the market of -0.3, and a beta coefficient of -1.5.

Security B has an expected return of 12%, a standard deviation of returns of 10%, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier?

Why?

#6-4

Suppose you owned a portfolio consisting of $250,000 of government bonds with a maturity of 30 years.

a. Would your portfolio be riskless?

b. Now suppose you hold a portfolio consisting of $250,000 of 30-day Treasure bills. Every 30 days your bills mature, and you reinvest the principal ($250,000) in a new batch of bill. Assume that you live on the investment income from your portfolio and that you want to maintain a constant standard of living. Is your portfolio truly riskless?

c. Can you think of any asset that would be completely riskless? What security comes closest to being riskless? Explain.

#6-5

If investors' aversion to risk increased, would the risk premium on a high-beta stock increase by more or less than that on a low-beta stock? Explain.

#6-6

If a company's beta were to double, would its expected return double?

Problems:

#6-1

Portfolio Beta

An individual has $35,000 invested in a stock with a beta of 0.8 and another $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio, what is her portfolio's beta?

#6-2

Required Rate

of Return

Assume that the risk-free rate is 6% and that the expected return on the market is 13%. What is the required rate of return on a stock that has a beta of 0.7?

#6-4

Expected Return:

Discrete Distribution

A stock's return has the following distribution:

Demand for the Probability of This Rate of Return if this

Company's products Demand Occurring Demand Occurs (%)

Weak 0.1 -50%

Below average 0.2 (5)

Average 0.4 16

Above average 0.2 25

Strong 0.1 60

1.0

Calculate the stock's expected return, standard deviation, and coefficient of variation.

#6-7

Required Rate of

Return

Suppose rRF = 9%, rM = 14%, bi = 1.3.

a. What is ri, the required rate of return on stock i?

b. Now suppose rRF (1) increases to 10% or (2) decreases to 8%. The slope of the SML remains constant. How would this affect rM and ri?

c. Now Assume rRF remains at 9% but rM (1) increases to 16% or (2) falls to 13%. The slope of the SML does not remain constant. How would these changes affect ri?

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#### Solution Preview

Please find attached file.

Questions:

1) What types of risk are measured by standard deviation and beta? Which type of risk is more important? Where does correlation fit in? Assume the market risk premium is 5%. Research a current stock and determine its required rate of return using the SML.

Since the standard deviation is basically a measure of an investment's volatility, the type of risk that is most widely measured using it is the market risk. This is so because one of the most unpredictable elements within investments is Market movement which is known to get volatile any time. The beta on the other hand, being a measure of volatility but only in comparison to a market index or benchmark, can be used to measure the market risk as well. However with the standard deviation not tied down to any specific benchmark, it can also be used to measure both default risk and foreign exchange risks.

The type of risk that is more important is the standard deviation. This is because the standard deviation gives an actual return on the fund, irrespective of whether it is in line with any set benchmark. The beta on the other hand may indicate an investment as performing well relative to the market, but in retrospect be underperforming given its own internal characteristics which state that it ought to be giving the shareholders a greater return and not simply beating the market.

Correlation in this instance fits in when comparing how two or more investments may be performing or behaving in respect to each other.

Market risk premium can be defined as the difference between an investment's risk-free rate and its expected returns within the market. The required rate of return however is the minimum rate of return that investors anticipate that their investment should return to them. The required rate of return is generally derived from the formula:

Ke= Krf + (Km-Krf)ß

In this instance, the risk free rate is usually the three month U.S. Treasury bill rate, which here will be set at 0.025%.

Required rate of return for Citigroup in this case would be:

Ke= Krf + (Km-Krf) ß

Ke= 2.5 + (5-2.5)2.56

Ke= 2.5 + 6.4

Ke= 8.9%

#6-3

Security A has an expected return of 7%, a standard deviation of returns of 35%, a correlation coefficient with the market of -0.3, and a beta coefficient of -1.5.

Security B has an ...

#### Solution Summary

A required rate of return, expected return and discrete distribution is examined.