A portfolio

A portfolio consists of £10,000 in each of 2 assets, x1, and x2,. The daily standard deviations are 1.3%, and 0.7%. The correlation between the returns of x1and x2 is 0.562. Calculate the Basle recommended VaR over a 10-day horizon and the recommended capital adequacy? [Hint: VaR(Basle) = Vp2.33?10?p]

The total value of the portfolio is £20,000 held as £10,000 in x1 and £10,000 in x2. The respective standard deviation of returns of the two assets are sx1 = .013 and sx2 = .007. The correlation of the returns ? = 0.562.
The risk on the portfolio sp is
s_p=v(?0.5)?^2 s_x1^2+(0.5)^2 s_x2^2+2(0.5)(0.5)?s_x1 s_x2
s_p=v(?.5?^2 (.013)^2+?.5?^2 ?(.007)?^2+2(.5)(.5)(0.562)(.013)(.007) )=0.0089482

Basle VaR = (20,000(2.33)(0.0089482)v10) = £1,318.63
Capital Adequacy = 3*Basel VaR = £3,955.90

A US investor holds $10m of AT&T shares and $5m of IBM shares. The daily volatility of AT&T shares is ?1 = 1.5%; and the daily volatility of IBM is ?2 = 1.0%. Calculate the variance of the portfolio and the Basle recommended VaR if the correlation between the returns of the 2 assets is a) ? = 1.0 and b) ? = -0.10.

? = 1.0
? = -0.10

For ? = 1.0

= $4.4 m

For ? = -.010

Think about why the VaR value is lower in the second case.

What is your dollar VaR when holding a UK portfolio of £100m if the current exchange rate is 1.5$ per £, the correlation between the return on the UK portfolio and the exchange rate is ? = 0.5, the standard deviation of the UK portfolio is?1 = 1.896% and the standard deviation of the exchange rate is ?2 = 3%.

This question does not specify the Basle requirement so we can take the standard 95% confidence level.

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