Question

Your investment portfolio consists of $10,000 shares of Dell. The expected return on Dell is 11%, with a standard deviation (volatility) of 43%. Suppose the risk-free rate is 4%, the expected return on the market is 9% and the volatility of the market is 18%.

a) Find a portfolio on the Capital Market Line has the same expected return as Dell. What is the volatility of that portfolio? What mix of the market portfolio and the risk-free asset would give you that portfolio?

b) Find a portfolio on the Capital Market Line has the same volatility as Dell. What is the expected return on that portfolio? What mix of the market portfolio and the risk-free asset would give you that portfolio?

c) Plot the capital market line, Dell, and the two portfolios that you identified above.

d) Plot the securities market line. If CAPM holds, based on the above information, what must be Dell’s beta? Plot Dell on the SML.

Answer 1

Average return from Capital market line is give by

Er = Rm×Wm + (1-Wm)×Rf

Where

Er = expected rate of of return = dell's return=11%

Rm= 9%

Wm= weight to the market portfolio in capital market line=??

Rf= risk free rate =4%

11=9×Wm+(1-Wm)×4

Wm= 1.4

1-Wm=1-.1.4= -.4

It means that to get 11% return from capital market portfolio we will have to borrow 40% money at risk free rate and invest 140% (i.e. 100% our money and 40% borrowed money) in market portfolio)

Volatility Of that porfotlio will be

SDc= SD of market × Wm as the SD of risk free asset is 0

So volatility = 1.4 ×18%=25.2%

Let us check whether our calculations are right?

CML is

Er= rf+ SDc×(Rm-Rf)/SDm

=4+25.2×(9-4)/18 =11%

Yes ! We were right

Part 2

we want CMl portfolio to have same SD as that of dell i.e. SDc= 43%

So SDc= SDm× Wm

43=18×Wm

Wm=2.38

1-Wm= 1-2.38=1.38

Which means that we will borrow 138% money at rf and invest

238% i.e. 100% own money and 138% borrowed money in market.

Expected return Er= 2.38×18 -1.38×4= 37.32%

Part c and d

Beta of dell as per CAPM is given by

11=4+(9-4)× beta

Beta= 1.4

CML and SML are as follows

APM