P2 Mock Exam C Q 15

[delta123]

HI David,
Here is the question 15
A $20 million portfolio is equally invested in two currencies: $10 million in US dollars (USD)
and $10 million in Euros (EUR). The volatility of the Euro (EUR) is 20%; the volatility of the
dollar (USD) is 30%. The two currencies have a correlation of 0.60. What is the beta of the
US dollar (USD) position with respect to the two-asset portfolio that includes the US dollar
position; i.e., beta (USD, Two-asset Portfolio)?
a) 0.75
b) 1.00
c) 1.25
d) 1.50

I am trying to solve this question other way.

Beta (USD, Portfolio) = Covariance(USD, Portfolio)/Variance(Portfolio).
Beta (USD, Portfolio) = Corelation(USD)*Vol(USD)*Vol(Portfolio)/Variance(Portfolio).

Variance (Portfolio) = 0.5^2 * 20%^2 + 0.5^2 * 30%^2 + 2 * 0.5 * 0.5 * 20% * 30% * 0.6

= 0.0505
Vol(portfolio) =.2247

Beta (USD, Portfolio) =.6*.3*.2247/.0505 =0.80

Can you please help why I am not getting right answer 1.25 which is in the solution set.

Thanks,

 

[k.simpson]

You have: Beta (USD, Portfolio) = Corelation(USD)*Vol(USD)*Vol(Portfolio)/Variance(Portfolio).

The correlation of the USD investment with the portfolio is not 0.6. I think that is the part you are confusing. To use your method, you would need to have the correlation rho(USD, portfolio). What you have used is rho(USD, EUR).

Calculating the correlation rho(USD, portfolio) is practically as hard as calculating the covariance (at least based on the info given in the question). I think the covariance way might actually be simpler (at least IMO).

 

[delta123]

thanks k.simpson. It make sense.

 

[David Harper CFA FRM]

It is a good question and it's instructive, I think k.simpson is right: we want beta(USD, Portfolio) which simplifies to correlation(USD,Portfolio)*volatility(USD)/volatility(Portfolio). I'm not even sure what is a direct way to retrieve that correlation, but it somewhat circular fashion, we can infer that it is 0.0630 cov(USD,P)/(20%*22.47%) = 0.9345, with beta(USD,Portfolio) = 0.9345*30% USD vol/22.47% Portfolio vol = 1.2475, in self-serving cicularity

Here is the source question @ http://forum.bionicturtle.com/threa...-component-value-at-risk-var.4779/#post-12611

Per our learning XLS, I show two ways to reach beta(USD, P):

1. Beta, via (%) = Covariance (USD,P) / Variance(P), as shown
2. Beta, via ($) = W * Dollar Covariance (USD,P) / Dollar Variance(P) = $20.0 million * 1.260 Cov$(USD,P) / 20.20 variance$(P). Thanks,

(cross-posted ....)