Suppose you’ve estimated that the fifth-percentile value at risk of a portfolio is $\230%$. Now you wish to estimate the portfolio’s first-percentile VaR (the value below which lie $1\%$ of the returns). Will the $1\%$ VaR be greater or less than $230\%$?

Value at risk (VAR) has become a key concept in financial calculations. The VAR of an investment is defined as that value v such that there is only a 1 percent chance that the loss from the investment will exceed v. (a) If the gain from an investment is a normal random variable with mean 10 and variance 49, determine the value at risk. (If X is the gain, then −X is the loss.) (b) Among a set of investments whose gains are all normally distributed show that the one having the smallest VAR is the one having the largest value of $\mu-2.33 \sigma,$ where $\mu \text { and } \sigma^{2}$ are the mean and variance of the gain from the investment.

You’ve borrowed $20,000 on margin to buy shares in Ixnay, which is now selling at$40 per share. Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the stock price falls to $35 per share. How low can the price of Ixnay shares fall before you receive a margin call?

You are bullish on Telecom stock. The current market price is $50 per share, and you have$5,000 of your own to invest. You borrow an additional $5,000 from your broker at an interest rate of 8% per year and invest$10,000 in the stock. a. How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately.

You are bullish on Telecom stock. The current market price is $50 per share, and you have$5,000 of your own to invest. You borrow an additional $5,000 from your broker at an interest rate of 8% per year and invest$10,000 in the stock. a. What will be your rate of return if the price of Telecom stock goes up by 10% during the next year? (Ignore the expected dividend.)

The average rate of return on investments in large stocks has outpaced that on investments in Treasury bills by about 7% since 1926. Why, then, does anyone invest in Treasury bills?

Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $40 per share. She borrows$4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8%. What is the rate of return on her investment?

On January 1, you sold short one round lot (that is, 100 shares) of Snow’s stock at $21 per share. On March 1, a dividend of$3 per share was paid. On April 1, you covered the short sale by buying the stock at a price of $15 per share. You paid 50 cents per share in commissions for each transaction. What is the value of your account on April 1?

Suppose that you sell short 500 shares of XTel, currently selling for $40 per share, and give your broker$15,000 to establish your margin account. If you earn no interest on the funds in your margin account, what will be your rate of return after one year if XTel stock is selling at

$44

Suppose that you sell short 500 shares of XTel, currently selling for $40 per share, and give your broker$15,000 to establish your margin account. If you earn no interest on the funds in your margin account, what will be your rate of return after one year if XTel stock is selling at

$40

Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $40 per share. She borrows$4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8%. If the share price falls to $30 per share by the end of the year, what is the remaining margin in her account? If the maintenance margin requirement is 30%, will she receive a margin call?

Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $40 per share. She borrows$4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8%. What is the margin in Dée’s account when she first purchases the stock?

Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $\$40$ per share. She borrows $\$4,000$ from her broker to help pay for the purchase. The interest rate on the loan is $8\%$.

a. What is the margin in Dée’s account when she first purchases the stock?

b. If the share price falls to $\$30$ per share by the end of the year, what is the remaining margin in her account? If the maintenance margin requirement is $30\%$, will she receive a margin call?

c. What is the rate of return on her investment?

You are bearish on Telecom and decide to sell short 100 shares at the current market price of $\$50$ per share.

a. How much in cash or securities must you put into your brokerage account if the broker’s initial margin requirement is $50\%$ of the value of the short position?

b. How high can the price of the stock go before you get a margin call if the maintenance margin is $30\%$ of the value of the short position?