Question

Imagine that you are managing a trading portfolio with 100 shares of stock in Samsung. The current price is 12,800 Won (the South Korean currency). The standard deviation of the daily return on Samsung estimated over the past 3 months is 1 percent. The $/Won exchange rate is currently 1/980 (that is $1 = 980 Won), and the standard deviation of the exchange rate (in percentage terms) is 0.4% per day, again using the past 3 months of data. Also, the correlation between the percentage change in the exchange rate and the return on Samsung is estimated to be equal to 0.5. Use delta normal to compute the 1-day, 99% VAR for the portfolio from the perspective of a US bank (i.e. in US dollars).

a) $38
b) $44
c) $48
d) $52
e) $56

Answer 1

The 1-day, 99% VAR for the portfolio is approximately $7.24.

Step-by-step explanation:

To calculate the Value at Risk (VAR) for the portfolio, we need to take into account the volatility of both the stock price and the exchange rate. The VAR is calculated using the formula: VAR = Portfolio Value x Z-Score x Standard Deviation of the Portfolio's Return, where Z-Score is the number of standard deviations corresponding to the desired confidence level.

First, we need to convert the stock price from Won to USD using the exchange rate. The converted stock price is $12.24 (12,800 Won / 980). Then, we calculate the daily return on the stock as the percentage change in price: (12.24 - 12.8) / 12.8 = -0.04375 (-4.375%).

Now, we calculate the daily VAR using delta normal approximation:
VAR = Portfolio Value x Z-Score x Standard Deviation of the Portfolio's Return = 100 x 1.65 x (-0.04375) = -7.24 USD.

Since we are only interested in the positive loss, we take the absolute value of the VAR: 7.24 USD. Therefore, the 1-day, 99% VAR for the portfolio is approximately $7.24.