April 2012, Q2

In a market where the CAPM holds there are five risky assets with the following attributes per year.

Asset number 1 2 3 4 5
Expected Return 6% 5% 8% 13% 11%
Market capitaln ($) 2.6m 3.9m 5.2m - 1.3m
Beta - - - 1.5 -

The risk-free rate is r = 1% p.a.

(i) Calculate the expected return on the market portfolio. [1]
(ii) Deduce the market capitalisation of asset 4 and the betas of all the other assets. [3]
(iii) Calculate the beta of a portfolio P which is equally weighted in the five assets and the risk-free asset. [1]
(iv) Explain whether or not this portfolio P lies on the Capital Market Line. [2]

Im good for part (i). For part (ii), where does the market capitalisation figure & beta figures get calculated from? Which formula in particular?

 

I'm sure a tutor will weigh in with the correct, clearer, more thorough solution... but, as you have calculated the return on the market portfolio, this return should be equal to the "weighted by market capitalisation" return of the individual assets. This is because CAPM hold and we are assuming the portfolio is efficient => the separation theorem holds.

The beta figures can be calculated from the expected return on the market and expected return on each asset:

E[asset] = r + beta(E[market] - r)

Chris

 

Thanks pma99car... Much obliged

 

How do you get (i)?

The examiners solution is way too short.

 

Gosh. I did not get i) please help!

 

For part (i), use the equation for the Security Market Line (this is on p43 of the Tables if you need a reminder) together with the info provided about Asset 4.

 

Tks a mil! I really couldnt see the truth before me..

 

Hi I'm wondering if anyone can help with the exact working of the market capitalisation for asset 4 here? I'm just not getting the answer and even when I work backwards I'm not getting the expected return on the market portfolio of 9% found in part i.

And then can someone possible explain how to go about part 3 of this question. I calculated the expected return assuming an equal weighting of 0.2 and substituted this into the equation for the security line but I think I may have misunderstood what they mean by "equally weighted".

Thank you in advance

Antoinette