An investor is evaluating two investments: a risk-free asset and the common stoc

Question

An investor is evaluating two investments: a risk-free asset and the common stock of Schallheim Inc. The investor is going to construct a portfolio consisting of the risk-free asset and Schallheim's stock. The following table shows the various portfolio expected return and beta combinations that could be achieved by his portfolio.

PErcentage of port.            Portfolio                    Portfolio BEta
in Schallheim                      Expected Ret.

0%                                      5.5%                          0.0
25%                                    6.75%                        .25
50%                                    8%                             .50
75%                                    9.25%                        .75
100%                                  10.5%                        1.00
125%                                  11.75%                       1.25

What is the reward-to-risk ratio for Schallheim's stock?

6%
7%
8.0%
9%
5%
8.00%

Merton Corp. has a higher beta than Schallheim Inc. Both stocks trade in the same market. Which of the following most accurately describes Merton's reward-to-risk ratio? Assume the market is efficient.

Merton's reward-to-risk ratio is lower than Schallheim's ratio.
Merton's reward-to-risk ratio is higher than Schallheim's ratio.
Merton's reward-to-risk ratio is the same as Schallheim's ratio.

Explanation / Answer

Letx be the return on Schallheim and y be the risk free rate
Hence,
@25% in Scallheim: 0.25x+0.75y=13.5
@50% in Scallheim: 0.5x+0.5y=8

So,
y=5.5%
x=10.5%

Portfolio beta @25% in Scallheim=0.25*beta
Given this is 0.25 so beta of scllheim=1

Reward to risk ratio=(Return-Rf)/beta=(10.5%-5.5%)/1=5

As per CAPM, return=risk free+beta*market risk premium

So, reward to risk ratio=(return-riskfree)/beta=(riskfree+beta*market risk premium-risk free)/beta=market risk premium

Now this is same for every stock hence Metron's risk reward ratio is the same as Scllheim's ratio

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