BKM Ch$5$ problems $1,2,13,16$

Suppose you've estimated that the $5$ th$-$percentile value at risk of a portfolio is $-30\%.$ Now you wish to

estimate the portfolio's $1$ st$-$percentile VaR. Will the $1\%$ VaR be greater or less than $-30\%?$

The real interest rate approximately equals the nominal rate minus the inflation rate. Suppose the inflation rate

increases from $3\%$ to $5\%.$ Does the Fisher equation imply that this increase will result in a fall in the real rate of

interest?

For both problems $13$ and $16,$ assume that you manage a risky portfolio with an expected rate of return of $17\%$

and a standard deviation of $27\%.$ The risk$-$free tbill rate is $7\%.$

Suppose a client of yours decides to invest in your risky portfolio a proportion $y$ of his total investment

budget, so that his overall portfolio will have an expected rate of return of $15\%.$

a$)$ What is the proportion $y?$

b$)$ If your risky portfolio consists of $27\%$ stock $A,33\%$ stock B$,$ and $40\%$ stock C$,$ what are your client's

investment proportions in $A,B,C,$ and tbills?

c$)$ What is the standard deviation of your client's portfolio?