Answer to Question #122116 in Finance for lastone

Question

The company has invested $400,000,000 in stocks and $600,000,000 in bonds. Stocks has a standard of 7%, while bonds have 10%. The correlation between stocks and bonds is 0.10. Calculate the portfolio VaR (DEAR) at 99% given mean of 10%.

Calculate the 1-year expected loss of a $100 million portfolio comprising 10 B-rated issuers. Assume that the 1-year probability of default for each issuer is 6% and the average recovery value for each issuer in the event of default is 40%.

Answer 1

1.Determine the standard deviation of portfolio returns:

according to the formula:

0.4, 0.6 - weight in securities portfolio

0.07, 0.1 -

standard deviation

$\sigma=(0.4^2\times0.07+0.6^2\times0.1+2\times0.4\times0.6\times0.07\times0.1\times0.1)^{1/2}=(0.0112+0.036+0.000336)^{1/2}=0.047536^{1/2}=0.2180$

A confidence level of 99% corresponds to 2.33 standard deviations.

According to the formula, we determine the portfolio VaR:

Portfolio VaR for a given 'confidence level is determined by the following formula:

where VaRP - VaR portfolio;

PP - the value of the portfolio;

sigma p - standard deviation of portfolio returns corresponding to the time for which VaR is calculated;

z a - the number of standard deviations corresponding to the level

confidence probability.

$Var=Pp\times\sigma p\times za$

$Var=100\times0.2180\times2.33=50.80$

2.

Calculate expected annual loss

$ECL=E(b)×E(CE)×E(LDG)$

Eb - probability of default

E(CE) - expected credit exposure

E(LDG) - expected severity

$0.06\times100\times 0.6 = 3.6$

unexpeted loss:

The loss distribution is a random variable with two states: default (loss of $60M, after recovery), and no default (loss of 0). The expectation is $3.6M. According to the variance formula of the random value

$0.06 \times(60-3.6)^2 + 0.94 \times (0-3.6)^2 =203.04$

The unexpected loss is therefore

Standard deviation:

$\sqrt{203.04} = 14.25$