Calculation of Beta

[Bester]

I have a question from GARP 2014 practice exam.

Suppose the S&P 500 has an expected annual return of 7.6% and volatility of 10.8%. Suppose the Atlantis Fund has an expected annual return of 8.3% and volatility of 8.8% and is benchmarked against the S&P 500. If the riskfree rate is 2.0% per year, what is the beta of the Atlantis Fund according to the Capital Asset Pricing Model?

a. 0.81
b. 0.89
c. 1.13
d. 1.23

Correct answer: c

Explanation: Since the correlation or covariance between the Atlantis Fund and the S&P 500 is not known, CAPM

must be used to back out the beta: −

= + ∙( − ).

Therefore:

8.3% = 2.0% + ∙(7.6% − 2.0%); hence = (8.3% − 2.0%) or 1.13.


Question:
Why can one not assume relative risk (i.e alpha) is equal to absolute risk
where absolute risk is calculated as 8.3% (Atlantis Fund Portfolio return) - 7.6% (S&P 500 Benchmark return) =0.7%

Thus to calculate Beta,

0.7% = 8.3% - 2% - Beta(7.6% -2%)
hence Beta = 1% (and not 1.13 as per Garp practice exam)

 

[ami44]

Hi,

In your logic β can never be anything else then 1.
You set α = Rfund - Rm
and then
α = Rfund - Rf - β * (Rm - Rf)
both together:
Rfund - Rm = Rfund - Rf - β * (Rm - Rf)
which you can transform in
Rm - Rf = β * (Rm - Rf) which means β = 1 whatever the values of the returns are.

You don't need to calculate any alpha. An alpha is a derivation from the CAPM. Alpha is a measure of how much you deviate from a Benchmark or the CAPM.
For this question you should assume, that the CAPM applies, i.e. that the Portfolio return is given by Rp = Rf + β * (Rm - Rf)

 

[Bester]

Thanks for the help