Statement I is correct - since forward prices are determined as (Spot - PV of dividends)*e^(rt), an increase in dividends will reduce forward prices.

Statement II is incorrect as forward prices will be determined by near term interest rates, specifically by the borrowing rate for the period of the contract, and will stay unchanged if near term interest rates do not change.

Statement III is incorrect. Futures exchanges require both buyers and sellers to deposit initial margins as prices can move adversely for either of them.

Statement IV is incorrect, as the margin deposited when a contract is entered into is called initial margin. Margin calls thereafter resulting from movements in prices are called variation margin.

Statement V is incorrect. Most futures exchanges distinguish between hedgers and speculators and require different margins from each.

Statement VI is incorrect. Interest rate futures behave almost identically to their bond counterparts, and carry both duration and convexity.

An option on a futures contract is like any other option contract, and only the option premium is due upfront. If the option is exercised, then the futures contract comes into existence and futures margins become due in the normal way. Therefore Choice 'b' is the correct answer.

https://riskprep.com/images/stories/questions/102.07.a.png  is the coefficient of risk aversion at x. Its inverse, ie  https://riskprep.com/images/stories/questions/102.07.b.png , is called the coefficient of risk tolerance.

Risk aversion or risk tolerance is indicated in a utility function by its curvature. A concave utility function indicates risk aversion and a convex function indicates risk tolerance. The curvature is measured as a ratio of the second derivative to the first derivative of a function. A negative second derivative implies concavity. The expression - is the coefficient of risk aversion, and its inverse, which is in the same units as wealth, is called the coefficient of risk tolerance.

The 'running yield' refers to the coupon rate divided by the current price. In this case, it is 6/96 = 6.25%. Remember that the running yield is also called the current yield.

According to ISDA, a credit event is an event linked to the deteriorating credit worthiness of an underlying reference entity in a credit derivative. The occurrence of a credit event usually triggers full or partial termination of the transaction and a payment from protection seller to protection buyer. Credit events include

- bankruptcy,

- failure to pay,

- restructuring,

- obligation acceleration,

- obligation default and

- repudiation/moratorium.

Therefore all four events listed are credit events and Choice 'b' is the correct answer.

The efficient frontier is plotted on a graph with portfolio return (mean) as the y-axis and portfolio volatility, or standard deviation, on the x-axis. Asset beta and standard deviation of the market portfolio have nothing to do with the determination of the efficient portfolio. Therefore Choice 'd' is the correct answer, and the rest of the choices are incorrect.

We need to calculate the total dollar duration of the bond portfolio, which is =100*7.5 - 65*12 + 120*6 = $690m. This means a 10 basis point change in interest rates changes the value of the portfolio by $690m*10bps = $0.69m, or $690,000. Therefore Choice 'b' is the correct answer.

[Here is an alternate step-by-step way of thinking about it. Let us consider changes to each position separately.a. A long position worth $100m in a bond with a modified duration of 7.5A 1% increase reduces the value of the bond by 7.5%. Therefore a 10bps = 0.1% change in interest rates will change the position by 0.75% = $100m*0.75% = $750,000 decrease.b. A short position worth $65m in a bond with a modified duration of 12A 1% increase increases the value of the position by 12% (remember this is a short position). Therefore a 10bps = 0.1% change in interest rates will change the position by 1.2% = $65m*1.2% = $780,000 increase.c. A long position worth $120m in a bond with a modified duration of 6A 1% increase reduces the value of the bond by 6%. Therefore a 10bps = 0.1% change in interest rates will change the position by 0.6% = $120m*0.6% = $720,000 decrease.The net change in the value of the porfolio is therefore:-750,000 + 780,000 - 720,000 = $690,000]

[Here is an alternate step-by-step way of thinking about it. Let us consider changes to each position separately.

a. A long position worth $100m in a bond with a modified duration of 7.5

A 1% increase reduces the value of the bond by 7.5%. Therefore a 10bps = 0.1% change in interest rates will change the position by 0.75% = $100m*0.75% = $750,000 decrease.

b. A short position worth $65m in a bond with a modified duration of 12

A 1% increase increases the value of the position by 12% (remember this is a short position). Therefore a 10bps = 0.1% change in interest rates will change the position by 1.2% = $65m*1.2% = $780,000 increase.

c. A long position worth $120m in a bond with a modified duration of 6

A 1% increase reduces the value of the bond by 6%. Therefore a 10bps = 0.1% change in interest rates will change the position by 0.6% = $120m*0.6% = $720,000 decrease.

The net change in the value of the porfolio is therefore:

-750,000 + 780,000 - 720,000 = $690,000]

The forward price for a commodity is nothing but the spot price plus carrying costs till the maturity date of the forward contract. Any increase in carrying costs therefore has the effect of increasing the forward price. Note that carrying costs include interest cost in respect of funding the position, costs of storage, less any convenience yield.

Increase in the carrying costs will not affect the spot prices.

The dividend payment has a present value of $2.20*e^( -6%*6/12) = $2.14. Therefore the forward price for delivery 9 months hence should be ($102 - $2.14)*e^(7%*9/12) = $105.25

The Sharpe ratio does not require investors to be risk neutral, only that for a given level of returns they prefer less risk to more risk. (Risk neutral means that investors are indifferent to the level of risk, and are only driven by a desire to maximizing expected value, regardless of risk levels.)

The ability to borrow and lend any amounts of money at the risk free rate is a fundamental assumption for the rule that optimal portfolios will maximize the Sharpe ratio.

This rule also assumes that risk preferences are completely described by return and standard deviation of returns.

Therefore Choice 'd' is the correct answer as statements I and II are correct.