Pass the PRMIA PRM Certification 8006 Questions and answers with ExamsMirror

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.

In terms of beta, his exposure is $10m*0.7 = $7m. This exposure is long.  In order order to neutralize his long exposure, he needs to have an equal an identical short position with the same beta as this long position (of course, in the short direction).  We need to figure out how many contracts will have a beta equal to his held position.  (The beta of a futures contract is slightly different from 1 when compared to spot, but in the absence of other information in the question it is always okay to assume that the beta of the futures contract is 1.  Such precision does not matter because of other errors such as rounding etc that cannot be anyway done away with.)

He needs to short futures contracts on the index with $7m in notional value. The value of each contract is currently 1000*250 =$250,000. He therefore needs to short $7m/$250,000 = 28 contracts to become market or beta neutral.

Investors have differing view of the market, which means differing view of expected returns, correlations and volatilities. Not only do they have differing views, these views change frequently as new information reveals itself. Accordingly, each investor has their own version of the efficient frontier. Once investors have determined their efficient frontiers, they will determine the extent of risk they wish to hold. If they had identical views, they would have held the same portfolio. But they do not, and if they did, there would be very little trading in the markets.

All the above statements are true except statement I which is false due to differing investor expectations.

(Re statement IV: If investors have different risk appetites, their portfolio will vary in the split between the risky and the riskfree assets. But inside the 'risky' assets bundle the proportion of the assets will be identical. Ie, they would express their varying risk appetites by varying how much of the risky bundle and the riskfree asset they hold, but inside the risky bundle the proportion of the different risky assets will be the same.)

The buyer of an FRA is considered 'long', and a 3 x 6 FRA allows him or her to borrow funds at the agreed rate starting at the end of month 3 till the end of month 6. (ie, 3 x 6 indicates that the borrowing period commences at 3 months, and ends at 6 months, for a period of 6 - 3 = 3 months). The seller has exactly the opposite position, ie he or she is committed to lend funds at the agreed rate for 3 months starting at the end of 3 months from today (for a 3 x 6 FRA). [Note that the obligation to borrow or lend in and FRA does not mean that either parties will actually do that, instead they will just exchange cash flows to get to get to an identical economic situation.]

Since the seller, or the short, is committed to lending in the future starting 3 months from now, it is akin to borrowing now for 3 months, and investing the borrowed amount for 6 months. During the first 3 months, the amounts borrowed and lent 'cancel' out (conceptually) and after the 3 months the short returns the amount borrowed, and is left with just the net amount lent, ie the FRA.

Thus the correct answer is Choice 'd'. Choice 'b' describes the position of the FRA buyer. Choice 'a' and Choice 'c' are nonsensical.

As a bond approaches maturity, its value will be driven less by the time value of money or its coupons, and more by its redemption value, ie the par. Therefore as maturity approaches, its value converges to its par value and this phenomenon is called pull to par.

The put-call parity makes sure that all else remaining equal, an increase in the value of a call option will be accompanies by an increase in the value of the corresponding put option.

Simply stated, the put-call parity can be expressed as:

Value of call - Value of put = Spot price - Exercise price discounted to the present

The two terms on the right hand side of this equation are fixed. Therefore, for the equality to be maintained, any increase in the value of the call option on the left hand side has to be accompanied by the value of the put.

Choice 'c' is therefore the correct answer.

To solve this question, we need to revisit how delta is calculated in a single step binomial model:

Consider a portfolio with just two positions: 1 Long Call option, and Δ Short Stock. We do not know what Δ (Delta) is.

Now if the current price of the stock is P, which can take the value P2 (higher value) and P1 (lower value) in the future at time T, then Δ needs to be such that the value of the portfolio is equal in both the cases. If the price goes up, the value of the option will be $1 (given) and the value of the short stock will be -Δ P2. If the price goes down, the value of the option will be $0, and the value of the stock will be -Δ P1.

Therefore, $1 - Δ P2 = $0 - Δ P1.

Solving for Δ, we get Δ = $1 /(P2 - P1) = $1 / ($102-$98) = 1/4.

T-bill futures 'discount' can be converted to a price for the bill using the formula Price = [1 - discount * number of days/360]. In this case, this works out to (1- 10% *90/360) * 100 = $97.50. Choice 'd' is the correct answer.

The futures price of the contract will be the future value of the spot price, calculated at a net rate equal to the cost of funding the futures position, less any dividends or other distributions. Also note that when rates are continuously compounded, Future Value = Present Value x (exp(rate x time)).

Therefore in this case the futures price for the S&P = 1000 * exp((5%-2%)*3/12) = 1007.53

The value of Bond 1 is $900,000 and the value of Bond 2 is $1,100,000, or their respective weights in the portfolio are 45% and 55% respectively. The combined duration is the weighted average of their individual durations, ie (45% x 5) + (55% x 10) = 7.75 years