Explanation
The effectiveness of the hedge is solely determined by the correlation between the position being hedged, and the position being used as the hedge. A hedge can be perfect when correlation is 1, and will be less than perfect when it is anything other than 1.The effectiveness of the optimal hedge is given by the formula (1-2), where is the correlation between the two. Therefore Choice 'c' is the correct answer. Standard deviations affect the hedge ratio, not the effectiveness of the hedge.

Explanation
Consider a long vanilla call at a strike of K1, and a short call with a strike price of K2 so that K2>K1. If you construct the payoff diagrams for these option positions, you will see that the combined payoff resembles very closely the payoff of a digital cash-or-nothing option. By bringing K2 and K1 closer together, we can make it very close to a digital cash-or-nothing option. Therefore Choice 'c' is the correct answer.

Explanation
The lowest achievable standard deviation will be lowest when the assets are perfectly negatively correlated, ie when correlation = -1. In the case of the above choices, the lowest correlation is -0.33, which is the correct choice.

Explanation
The most loss the fund manager can bear without facing a margin call is the loss that will make his margin balance account no lower than $4,000. This means he can have a loss of upto $1,000 before a margin call is triggered, implying that prices can fall by $10 per ounce (=$1,000/100 ounces per contract) without triggering a margin call. The margin call will be to top the margin up to the $5,000 initial margin.

Explanation
This question highlights the difference between zero rates, yield-to-maturity and forward rates. Forward rates are from one point in time to another, for example say from year 4 to 5 in the future. A zero rate is from time
0, or now, to a point in time in the future. The zero rate is dependent on the forward rates for all the different periods from now to the future. The yield curve represents the various zero rates at different points in time, and if it is upward sloping it means forward rates for years further out are greater than the years prior. That is what causes the zero rate yields to increase over time and the curve to slope upwards. So the forward rate from year
9 to 10 will certainly be higher than the 10 year zero rate.
The yield-to-maturity for a bond is the rate at which the payments on the bond discount to be equal to the current bond price. It is therefore the average rate that applies to the bond. This average is based upon the different zero rates for the years in which bond holders receive payments. Since coupons are smaller than the payment at maturity, the zero rate that applies to the payment at maturity will have the most impact on the numerical value of the bond's yield-to-maturity. Also affecting the yield-to-maturity will be the values of the coupon payments, which will be discounted at lower rates when the yield curve is upward sloping. So the yield-to-maturity will be an average lower than the 10 year zero. Since the 10 year zero will be lower than the forward rate from t=9-10, the yield-to-maturity will be the lowest rate of the three.