1. You would like to buy 1,000 shares of Google at a price of $200. To amplify your returns, you would like to buy on margin and borrow as much money as possible. The initial margin requirement is 80% and the maintenance margin requirement is 65%.

(a) What is the total amount of money you will borrow?

(b) At what price will you receive a maintenance margin call?

2. Using a stated annual percentage rate (APR) of 12%, compute the effective annual rates (EAR) for daily, monthly, quarterly, and semi-annual compounding periods.

3. A coupon bond that pays interest (coupon) semiannually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 6%. If the coupon rate is 8%, what is the intrinsic value of the bond today?

4. You are in charge of the bond trading and forward loan department of a large investment bank. You have the following YTMs for five default-free pure discount bonds as displayed on your computer terminal:

Years to maturity 1 2 3 5 10

YTMi 6% 6.5% 7% 6.5% 8% where YTMi denotes the yield to maturity of a default-free pure discount bond maturing at time i. (A) A new summer intern from Harvard tells you that 3 year treasury notes with annual coupons of $100 and face value of $1,000 are trading for $1,000. Would you ask the intern to recheck the price of this coupon bond? If so, why?

(B) What is the annualized forward interest rate between the end of year 3 and the end of year 5? In other words, what is the geometric average forward interest rate for years 4 and 5?

(C) If the expected one year short rate for year 2 (i.e., from year 1 to year 2) is 5%, then what is the liquidity premium for year 2?

5. You are hired by a bank to help them design a bond portfolio to fund a $10 million obligation that will come due in 4 years (money market deposits). The managers of the fund would like to use 2 year zero coupon bond along with their existing bond portfolio A that includes following three zero coupon bonds with the corresponding portfolio weight:

Security 5 year zeros 7 year zeros 10 year zeros Portfolio weight 25% 25% 50%

Suppose that the yield to maturity on all bonds is 5% (in other words, the yield curve is flat at 5%). 1) How much money do you have to invest today in the bond market to entirely fund your obligation?

2) What is the durations of current existing bond portfolio A and the obligation (due in 4 years).

3) How would you structure your holdings of the 2 year zero coupon bond and their existing portfolio A so that you are protected against the risk of interest rate fluctuations? Please indicate the dollar amount you would invest in each security.

I need these problems worked out step by step. Tell me which formulas were used for each one please. These are review problems and I want to make sure i get the steps right and use the correct formulas