Pass the PRMIA PRM Certification 8006 Questions and answers with ExamsMirror

According to the dividend discount model, the spot share prices represent the present value of all the future cash flows from the stock. If held till perpetuity, this becomes an annuity equal to the dividend, growing at its expected growth rate. Therefore Choice 'a' is the correct answer. Choice 'c' would represent the total market cap, and not the value per share that the question asks.

The loss to the fund manager is $20*100 = $2,000. The initial margin placed was $5,000. After the loss is charged to his account, the margin balance is only $3,000 ($5,000 - $2,000). The margin to be maintained is $5,000. Therefore the margin call is $2,000.

Note that there would have been no margin call till the balance in the margin account had reduced to the 'maintenance' level of $4,000. So if the price had fallen by $5, and the loss had been $500, there would have been no margin call. But when the margin call would be made, it would require the balance to be brought up to the initial margin of $5,000 (and not the maintenance margin of $4,000).

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-ρ2), where ρ is the correlation between the two. Therefore Choice 'a' is the correct answer. Standard deviations affect the hedge ratio, not the effectiveness of the hedge.

(Note: In other texts, hedge effectiveness is explained to be measured by ρ2, which is essentially the same as √(1-ρ2), both expressions being functions of ρ. You can use either, being aware that one measures the variance explained, and the other is a measure of the unexplained variance.)

The minimum variance hedge ratio answers the question of how much of the hedge to buy to hedge a given position. It minimizes the combined volatility of the primary and the hedge position. The minimum variance hedge ratio is given by the expression 103.10.b103.10.b. Effectively, this is the same as the beta of the primary position with respect to the hedge.

All other choices are incorrect.

Intuitive understanding of the hedge ratio: There are two standard deviations in play here: one, the standard deviation of the asset to be hedged (σx), and two, the standard deviation of the asset being used as the hedge(σy).  Now assume an extreme case where both the asset to be hedged and the asset being used as the hedge have a correlation of 1.  (That keeps the calculation simple.).  Also assume that the std dev of the asset to be hedged is 10% annually, and that of the asset being used as a hedge is say 20%.  At this point, just ignore all formulae, and think intuitively about how much of the hedge should we buy to have the same risk (in the opposite direction) as the primary position but in the opposite direction so the variation in the primary position is cancelled by opposite movements in the hedge position.  Obviously, we need to buy half because the asset being used as a hedge is twice as volatile.  In other words, we divided the volatility (std dev) of the primary position by the volatility of the asset being used as a hedge.In this question, σx is the standard deviation of the asset to be hedged, and σy is the standard deviation of the asset being used to hedge.  We will need to divide σx by σy.

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-ρ2), where ρ 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.

A residential mortgage carries a prepayment option for the borrower, where in the event of a decrease in interest rates they are likely to repay the mortgage and refinance at the new lower rate. If rates go up, the bank does not have a similar option. If the volatility of the underlying interest rates increases, mortgage holders are more likely to be faced with new rates that are sufficiently lower to persuade them to refinance. This reduces the ability of the bank to continue to earn the higher interest rate it was earning before.

Therefore an increase in volatility of the mortgage interest rates decreases the value of the mortgage portfolio.

The same rationale applies to callable bonds, where the borrower has the option to call the bond.

The maximum value for delta of a call option is 1 and not infinity. The value of theta for a deep out of the money call option does indeed approach zero as the value of the option is hardly affected by the passage of time. Vega measures the sensitivity of option prices to the volatility of the underlying, an increase in vega increases the price of the option regardless of whether it is a call option or a put option. (Vega is identical and positive for both calls and puts). Gamma changes very rapidly and reaches its maximum (& not zero) close to the strike price, including for a digital option. Therefore statement II is true and the rest are incorrect.

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.

The vast majority of exchange traded futures contracts are closed out prior to expiry by the parties acquiring offsetting positions. Very few contracts are settled by delivery. Since P&L on futures contracts is settled daily, 'cash settlement' really does not mean much as only the previous day's P&L is due or receivable on any given day.

Everything else remaining the same, an increase in the rate of dividends causes the value of call options to fall and the value of put options to rise. Therefore, Choice 'b' is the correct answer. (In the exam, the question could address either a call or a put option, so be aware of the answer in either case).

To understand this, consider how dividends are accounted for when valuing an option using the Black Scholes model. Future dividends are discounted to the present using the risk free rate and this discounted value is reduced from the spot price used in the BSM valuation. Effectively, this reduces the spot price used in the BSM formula. When the spot price reduces, and the exercise price remains the same, then the value of the call option goes down. In the same way, when spot price is reduced by the present value of dividends (and the exercise price stays the same), obviously the put option becomes more valuable. Therefore an increase in the rate of dividends increases the value of the put option.

There is another intuitive way to think about this: A call option is like a long position in the stock, but the holder of the call option is not entitled to receive dividends (unlike the holder of the stock). Since the holder of the call option has to forego the dividends, he is willing to pay less for the option; or in other words, the value of the call reduces.

In the same way, a put option is like having a short position in the stock. The holder of the short position has to borrow the stock in order to get into the short position in the first place. When dividends are paid, the holder of the short stock position has to make good any dividends that might be paid to the lender of the stock. The holder of a put option does not have to make any such payments. Therefore the put option is more valuable, and the existence of dividends (or an increase in dividends) increases the value of the put option.

(Try this out using the Black Scholes Excel model given under the tutorials by varying the spot price.)