Question

6-7

Require Rate of Return Suppose rRF = 5%, rM = 10%, and rA = 12%

a. Calculate Stock A's beta.

b. If Stock A's beta were 2.0, then what would be A's new required rate of return?

6-8

Require Rate of Return As an equity analyst you are concerned with what will happen to the required return to Universal Toddler Industries's stock as market conditions change. Suppose rRF = 5%, rM = 12%, and bUTI = 1.4.

a. Under current conditions, what is rUTI, the required rate of return on UTI stock?

b. Now suppose rRF (1) increases to 6% or (2) decreases to 4%. The slope of the SML remains constant. How much this affect rM and rUTI?

c. Now assume rRF remains at 5% but rM (1) increases to 14% or (2) falls to 11%. The slope of the SML does not remain constant. How would these changes affect rUTI?

Answer 1

It is problem on portfolio analysis. You are investing in a stock. Stock is a risky investment. You have to ascertain how much return is required to cover the risk. It is ascertained by using capital asset pricing model. In this model equation of security market line (SML) has been developed to ascertain the required return on a security.

In SML equation, a security is compared with return from a risk free investment. Government bond is considered as risk free asset. In reality no investment can exist which is totally risk free. But government bond has minimum risk. It is without any default risk. This risk arises from the issuers liquidity posotion. If the issuer fails to pay dues in time, then default risk will crop up. Government bond has no such risk. Here governmet is the controller of money supply. During liquidity crisis it can print notes and circulate in the economy.

With risk free return add risk premium. It will cover extra risk of the security. This premium is acertained by multiplying market portfolio premium and beta value of the security. Thus market portfolio and beta value requires explanation.

Market portfolio is developed by combining more than one securities that are available in the market. The securities are well diversified in nature. As a result company specific risks are neutralized. It is also known as unsystematic risk. Suppose a company has weak marketing department and second one is very strong in marketing. Here risk of weak marketing company will be compensated by security of strong marketing company. It is believed that a well diversified market portfolio of 30 or more securities can reduce unsystematic risk to zero.

Therefore only systematic risk is observed in market portfolio. This risk arises from factors outside the company. These factors affect all companies of the ecoomy. Inflation, recession, unemployment, drought, flood, war. political unrest, exchange market instabilioty are few such factors.

Impact of systematic risk on a security is measured by beta value. It is ascertained from correlation of change in market portfolio return and change in the security return. Beta value of a market portfdolio is 1. If your security has has 1.2 beta value, then it will mean 1% change in market return will cause 1.2% change in security return.

So ascertain premium of market portfolio. It is the excess of market portfolio return over the risk free return. Multiply risk premium of market portfolio and beta value of a security to get premium of the security. Thus formula is:

$\textup{Return of a security} = \textup{risk free return}+\textup{beta value}(\textup{market return} - \textup{risk free return})$

If rRF = Risk free return = 5%

rM = return of market portfolio

rA = return of security A

Then,

$\textup{rA}=\textup{ rRF} + \ss \left ( \textup{\textup{rM}} -\textup{rRF} \right )$

Here,

rA= 12%; rM=10% and rRF=5%, then

12% = 5% + beta ( 10% - 5%)

5% beta = 12% - 5%

Therefore,

Beta = 7% /5% = 1.4

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If beta of security A is 2 then return of security A should be:

$\textup{rA}= 5 \textup{percent} + 2\times \left ( 10 \textup{percent} - 5 \textup{percent} \right )$

      $= 5 \textup{percent} + 2\times 5 \textup{percent}= 15 \textup{percent}$

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Problem 6 -8

In this problem, consider following information.on security UTI:

$\textup{Risk fee rate} = \textup{rRF} = 5 \textup{percent}$

$\textup{Market return} = \textup{rM} = 12 \textup{percent}$

$\textup{Beta of UTI} = \textup{bUTI} = 1.4$

Therefore,

$\textup{rUTI} =5 \textup{percent} +1.4\left ( 12 \textup{percent} - 5 \textup{percent} \right )$

           $=5 \textup{percent} +1.4\times 7\textup{percent}$

           $=5 \textup{percent} +9.8\textup{percent}$

           $=14.8 \textup{percent}$

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Answer (b):

If you plot the SML equation in a diagram, then horizontal axis will measure beta value, and vertical axis will measure security return. So slope is ( rM - rRF) and intercept is rRF.

Now rRF is going up from 5% to 6%, It will increase intecept upward. As the slope is constant, the SML will shift parallay upward. As the slope is not changing then,

rM - rRF = 7%

rM = 7% +rRF

     = 7% + 6%

     = 13%

Thus rM is going up from 12% to 13% when rRF has increased from 5% to 6%

If rM has moved down from 5% to 4%, then

rM = 7% + 4% = 11%.

Thus it is coming down from 12% to 11%.

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Answer c:

Now rM has moved up from 12% to 14% and rRF remains constant at 5%, then slope of the sML will move up. Thus SML is steeper now. Thus new rUTI is:

rUTI = rRF + bUTI ( rM - rRF)

        = 5% + 1.4 ( 14% - 5%)

        = 5% + 1.4 x 9%

        = 5% + 12.6%

        = 17.6%

If rM = 11% then,

rUTI = rRF + bUTI ( rM - rRF)

       = 5% + 1.4 ( 11% - 5% )

       = 5% + 1.4 x 6%

       = 5% +8.4 %

       = 13.4%