Question

33. Assume the expected return on the market portfolio is 15% and its standard deviation is 12%. The risk-free rate is 5%. Denote the expected return and standard deviation of portfolios on the Capital Market Line (CML) with () and SD, respectively. Which statement on the CML is FALSE?
A) The Sharpe ratio of a CML portfolio that contain 150% of the market portfolio and 50% borrowed money is smaller than 1.

B) The CML can be represented by the following equation: () = 0.05 + .

C) The standard deviation of a CML portfolio that contains 50% savings and 50% of the market portfolio equals 12%.
D) The expected return of a CML portfolio that contains 150% of the market portfolio and 50% borrowed money is 20%.

Ans: C

Answer 1

Answer is option (C)

Explanation :-

In case of option C ,

Weight of market portfolio = 50% i.e, 0.5

And weight of savings or risk free asset = 0.50

Now standard deviation of CML portfolio = weight of market portfolio * standard deviation of market portfolio

= 0.5*12= 6%

Hence statement given in option C is false as standard deviation of CML portfolio given in question is 12%

Now option (D ) is not answer because Statement given in option (D) is true as expected return of CML portfolio = weighted average of returns of individual portfolio

Where,weight of market portfolio =150% i.e,1.5

And weight of borrowed money = 1-1.5=-0.5

Hence Expected return of CML portfolio =

1.5*15 - 0.5*5=20%

Option( A ) is also not the answer because Statement given in option A is also true as

Sharpe ratio=( Expected return of portfolio- Risk free rate )/Standard deviation

Where standard deviation = weight of market portfolio * standard deviation of market = 1.5*12=18%

Hence sharpe ratio= (20-5)/18=0.83 which is smaller than 1