PRMIA 8006 - Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition

Price quotes for futures where one of the currencies is the US dollar follow the convention of using the number of US dollars that one unit of the foreign currency can buy. (For JPY, 100 Yen is used.)

In the forward market, the convention used is the same as that used in the spot market.

In the spot market, prices are expressed as the number of units of the foreign currency that 1 USD can buy, except for GBP, EUR, AUD and NZD where it is the other way round (ie, number of USDs that 1 of each of these currencies can buy).

According to the CAPM, the expected return from a risky asset is a function of the contribution of the risky asset to the total risk of the market portfolio. Nothing else matters. All assets are priced according to the risk they bring to the market portfolio, regardless of their individual level of risk. An asset that is very volatile on its own, but has a negative correlation to the market may be priced high, ie have low expected return, because of its impact on the risk of the market portfolio. Therefore Choice 'a' is the correct answer, and the other options are incorrect.

Recall that according to the CAPM β = covariancex, y / variancex, where x is the market portfolio and y is the risky asset.

The beta itself is a function of the covariance of the asset's returns with market returns, and therefore only the driver of expected return for an asset is its beta, which is determined by the asset's contribution to portfolio risk. (β = covariance(x, y) / variance(x), where x is the market portfolio and y is the risky asset. )

Interest rate caps are effectively call options on an underlying interest rate that protect the buyer of the cap against a rise in interest rates over the agreed exercise rate. As with options, the premium on the cap depends upon the volatility of the underlying rates as one of its variables. A floor is the exact opposite of a cap, ie it is effectively a put option on an underlying interest rate that protects the buyer of the floor against a fall in interest rates below the agreed exercise rate. Therefore statements I and II are correct.

A cap protects a borrower against a rise in interest rates beyond a point, and a floor protects a lender against a fall in interest rates below a point.

A collar is a combination of a long cap and a short floor, the idea being that the premium due on the cap is offset partly by the premium earned on the short floor position. Therefore a collar is less expensive than a cap or a floor.

Caps, floors and collars provide a hedge against interest rate risks. Therefore statement III is correct too. However. they do not always provide protection against spreads changing, as the rate other than the one referenced by the cap or the floor may change causing the spread to change. Therefore statement IV is incorrect.

Professional management that acts as the agent of the shareholders is not likely to protect debt holders from a transfer of wealth to the shareholders. All other mechanisms listed are intended to offset the agency cost for debt holders, ie the expected cost that shareholders and management will transfer wealth away to the detriment of the debt holders.

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. For a given level of volatility, it identifies the portfolio with the maximum return. Therefore Choice 'b' is the correct answer.

If a reading is taken from the y-axis (ie returns) by dropping a perpendicular line on to the efficient frontier, we can get the minimum risk portfolio for the given level of returns. So the efficient frontier can be used to identify either the highest return per unit of volatility, or the lowest volatility given a desired level of returns. The efficient frontier does not describe the market portfolio, though the market portfolio may be one of the many points on the efficient frontier. Thus the other choices are incorrect.

The effect of higher convexity is that when yields rise, the price decrease is lower than the increase in yields, and when yields fall, the increase in price is greater than the fall in yield. In either case, it benefits the holder of the fixed income instrument that carries such positive convexity. The converse is true for someone short a bond - such an investor would prefer lower convexity to higher convexity. Therefore statement I is not true for an investor who is short a bond.

An increase in yields makes bond prices decrease, something that would benefit the short. Therefore statement II is true for an investor short a bond.

Negative convexity has exactly the opposite effect as the one described for positive convexity for statement I above. An investor short a bond would prefer negative convexity (which by the way is exhibited by very few fixed income instruments such as mortgages) to positive convexity, therefore statement III is true for such an investor.

Choice 'b' is the correct answer.

The equivalent continuously compounded rate in this case can be calculated as ln(1+5.2%) = 5.07%. The other answers are incorrect.

Refer to the tutorial on interest rates for more details on how continuously compounded rates work.

Macaulay duration is the weighted average of the present value of payments received on a bond, weighted by the year in which the payments are received. If the yield curve changes shape, it will change the present values of the coupons and therefore also the Macaulay duration. Statement I is therefore not correct. However, if the bond were to be a zero-coupon bond, changes in the curve will not affect its duration so long as the interest rate at maturity stays constant.

Modified duration = Macaulay Duration/(1 + rate/compounding frequency). Therefore modified duration will change if the compounding frequency changes, assuming the nominal rate of interest for the coupons are identical. Therefore statement II is correct.When rates are expressed as continuously compounded rates, modified duration and Macaulay duration will be identical. This intuitively follows from the formula for modified duration: Modified duration = Macaulay Duration/(1 + rate/compounding frequency). For continuously compounded rates, the compounding frequency approaches infinity, so the denominator approaches 1, leaving modified duration equal to the Macaulay duration. Therefore statement III is correct.

Convexity is higher for a bond that has its payments spread out compared to a bond that has its payments concentrated at a single point in time. For a bond with a higher coupon, the higher coupons have the effect of spreading the present value of the bond over a longer period, when compared to a bond with lower coupons where the payment is comparatively more concentrated at the maturity. Therefore Convexity is higher for a bond with a lower coupon when compared to a similar bond with a higher coupon. Statement IV is not correct.

The no-arbitrage futures price is given by exp(0.5*(4%-1%))*$1000 = $1015.11. Therefore Choice 'a' is the correct answer.

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]