Question

Treat each situation separately; show all calculations.
Critical value: 1.65(95%); 2.33(99%)

(a) You are holding a stock whose current value is s 4, 000.
Over the last year, histoncal data show that daily returns of this
share have averaged 0.012 percent per day, and the daily standard
deviation has been 0.06 percent. Assume that the daily retums
follow a normal distribution. At a 99% level of confidence, how
large a loss might occur on this stock luring the next 10
days?(Please consider both the absolute dollar loss and the loss
relative

to the expected profit).

(b) Currently your portfolio value is $60,000. According to
your estimation, the expected profit for your portfolio will be
$3,000 in the next year. If the yearly VAR(mean) at 99% confidence
level is $7, 500, at a 99% confidence, how large might the minimum
portfolio value and your absolute dollar loss of your portfolio be
in the next year?

(c) The VAR of XXx bank is $40 million under the RiskMetrics
system(95% confidence level, over one day). What is the VAR of XXX
bank under the Basel proposal(99% confidence level, over 10
days)?

d)a portfolio includes asset A and B. The weights in asset A
and B are 0.4 and 0.6. The returns of asset A and B are
independent. Asset A,'s daily VAR at 95% confidence level is S60.
The portfolio's daily VAR at 99% confidence is $110. What is the
Asset B's weekly

VAR at 99% confidence level?

(e) You have a $200 million portfolio invested in a bond If
over a month at the 99 percelevel of confidence, the yield will not
increase more than 0.3 percent and the portfol value will not be
lower than $194 million dollars, how large are the VaR and
modifie-duration of the bond?

Answer #1

**1.**

Current Value - 4000

Returns of the share - 0.012% per day

Standared Deviation - 0.06% per day

Level of Confidence - 99%

Calculate - Loss on stock during next 10 days

Loss on stock during next 10 days

Volatility in terms of $ shall be

1% of $ 4000 = 40

The Maximum loss for 1 day at 99% confidence level

$ 4000 * 2.33 = $ 9320

and expected maximum loss for 10 days shall be

10 * 9320 = 2947

Loss relative to expected profit = 4000*0.012*10 = 480

Total Loss for 10 days = 2947+480 = 3427

As a portfolio manager for Bank of America Merrill Lynch, you
are managing a portfolio of $48.50 million. You would like to
estimate how much your portfolio might be losing over the next 9
trading days. Suppose the portfolio has a daily volatility of
2.5%.
a. What is 9 day volatility? (sample answer: 15.50% or
0.1550)
b. What is the VaR (in dollars) over a 9 day time period at a 95%
confidence level?

As a portfolio manager for Bank of America Merrill
Lynch, you are managing a portfolio of $48.50 million. You would
like to estimate how much your portfolio might be losing over the
next 9 trading days. Suppose the portfolio has a daily volatility
of 2.5%.
a. What is 9 day volatility?
(sample answer: 15.50% or 0.1550)
b. What is the VaR (in dollars) over a 9 day time period
at a 95% confidence level?
(Sample answer: $2.5 million; or
$2,500,000.0)

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