8006 Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition Questions and Answers

Futures initial margins are determined by the exchange. SPAN is the name of a framework the CME uses to determine margins. Only Choice 'd' is correct.

An increase in coupon brings the 'average' cash flows closer, thereby decreasing duration. The higher the coupon, the lower the duration.

An increase in yield discounts the cash flows that are further away more than it does the closer cash flows, so an increase in yield decreases duration.

An increase in coupon frequency brings the bond's cash flows closer, thereby decreasing duration. Decreasing the coupon frequency has the opposite effect.

An increase in maturity pushes the payments further out, thereby increasing duration.

The swap can be valued by using the new swap rate of 5%. The investor is paying fixed and receiving LIBOR, and can effectively get out of his position by entering into a swap to receive 5% and pay LIBOR. This will leave him/her with a net cash flow of 1% for two years, ie $1m for 2 years that can be discounted to the present using the rates provided, ie =(1/1.05 + 1/(1.05^2)) = $1,859,410.

Detailed explanation:

An Interest Rate Swap exchanges fixed interest flows for floating rate flows. The floating rate leg is tied to some reference rate, such as LIBOR. The parties exchange net cash flows periodically. Conceptually, an interest rate swap is the combination of a fixed coupon bond and a floating rate note. The party receiving the fixed rate is long the fixed coupon bond and short the FRN, and the party receiving the floating rate is long the FRN and short the fixed coupon bond.

An interest rate swap can be valued as the difference between the two hypothetical bonds. FRNs sell for par at issue time as they pay whatever the current rate is, subject to periodic resets. Therefore immediately after a payment is made on a swap, the value of the FRN component is equal to its par value. The bond can be valued by discounting its cash flows. The difference between the two represents the value of the swap. When the swap is entered into, the fixed rate leg is set in such a way that the value of the hypothetical bond is equal to that of the FRN, and the swap is valued at zero. The rate at which the fixed rate leg is set is called the swap rate. Over its life, market rates change and the value of the fixed coupon bond equivalent in our swap diverges from par (whereas the FRN stays at par - at least right after payments are exchanged and the new floating rate is set for the next period). Thus the swap acquires a non-zero value.

There are two ways to value a swap. If interest rates for the future are known, the bond and the FRN can be valued and their difference will be equal to the value of the swap. Sometimes, the current swap rates are known. In such a case, the swap can be valued by imagining entering into an opposite swap at the new swap rate, which will leave a residual fixed cash flow for the remaining life of the swap. This residual cash flow can be valued and that represents the value of the swap. For example, if a 4 year swap was entered into exchanging an annual fixed 5% payment on a notional of $100m for a floating payment equal to LIBOR, and at the end of year 1 the swap rate is 6%, then the party paying fixed can choose to enter into a new swap to receive 6% and pay LIBOR. All cash flows between the old and the new swap will offset each other except a net receipt of 1% for the next 3 years. This cash flow can be valued using the current yield curve and represents the value of the swap.

The bond equivalent yield for a treasury bill can be calculated as [(Future value - Present value)/Present value x 365/days to maturity]. In this case this works out to ($100-$98)/$98 * 365/90 = 8.28%

[Why do we use 365 days and not 360? And is there a different way to calculate treasury bill yields?

The answer to this question is that there are alternate ways to calculate these yields. For the exam, I would suggest that you calculate according to one method, see if you get an answer that matches, and pick that. I found the below on the NY Fed's website - a very clear example: (http://newyorkfed.org/aboutthefed/fedpoint/fed28.html)

The Discount Yield Method

The following formula is used to determine the discount yield for T-bills that have three- or six-month maturities:

Discount yield = [(FV - PP)/FV] * [360/M]

FV = face value

PP = purchase price

M = maturity of bill. For a three-month T-bill (13 weeks) use 91, and for a six-month T-bill (26 weeks) use 182

360 = the number of days used by banks to determine short-term interest rates (the investment yield method is based on a calendar year: 365 days, or 366 in leap years).

Example

What is the discount yield for a 182-day T-bill, auctioned at an average price of $9,659.30 per $10,000 face value?

Discount yield = [(FV - PP)/FV] * [360/M]

FV = $10,000 PP = $9,659.30 M = 182

Discount yield = [(10,000) - (9,659.30)] / (10,000) * [360/182]

Discount yield = [340.7 / 10,000] * [1.978022]

Discount yield = .0673912 = 6.74%

For the 13-week bill, the same formula would be used, dividing 360 by a maturity of 91 days rather than 182 days.

The Investment Yield Method

When comparing the return on investment in T-bills to other short-term investment options, the investment yield method can be used. This yield is alternatively called the bond equivalent yield, the coupon equivalent rate, the effective yield and the interest yield.

The following formula is used to calculate the investment yield for T-bills that have three- or six-month maturities:

Investment yield = [(FV - PP)/PP] * [365 or 366/M]

Example

What is the investment yield of a 182-day T-bill, auctioned at an average price of $9,659.30 per $10,000 face value?

Investment yield = [(FV - PP)/PP] * [365/M]

FV = $10,000 PP = $9,659.30 M = 182

Investment yield = [(10,000 - 9,659.30) / (9,659.30)] * [365/182]

Investment yield = [340.70] / 9,659.30] * [2.0054945]

Investment yield = .0707372 = 7.07%

For the 13-week bill, the same formula can be used, dividing 365 (or 366) by a maturity of 91 days.

Explanation:

Notional principals are not exchanged at the start and the end of an FRA. In fact, if the notional principals were to be exchanged, it would increase credit risk and not decrease it by introducing settlement risk. Therefore Choice 'd' is incorrect.

All other choices correctly describe various aspects of an FRA.

Statement I is not correct because the 4% bond with the same modified duration as the zero coupon bond will have a maturity much later in the future than the zero coupon, and the final repayment coming much later will cause its convexity to be greater than the equivalent duration zero coupon bond.

Statement II is not correct as the convexity of a bond increases not in a linear fashion but in proportion to the square root of time as the maturity of the bond is increased.

Statement III is not correct as mortgage based bonds bring negative convexity even in the case of long positions,

Statement IV is not correct as the duration of a zero coupon bond maturing in 10 years has a modified duration greater than that of a coupon bearing bond of the same maturity, which means its convexity is higher and not lower (note this is different from statement I where the modified durations were identical. Here, the maturity is identical which has different implications.)

Therefore none of the statements is correct and Choice 'd' is the correct answer.

Choice 'a' is the correct answer as the issue of the floating rate note will provide the utility with the funds it needs, and the interest rate swap would offset the floating rate payment and leave it with a net fixed payment.

Choice 'd' is incorrect as the swap is in the wrong direction.

Choice 'c' is incorrect as buying and selling a floating rate bond would mean the utility will not have any funds that it wants to issue the note for, and combining it with interest rate futures would be just absurd.

Choice 'b' is incorrect as buying a floating rate note would use funds while the utility is trying to raise funds.

Since the 10 year rate has stayed the same, but the curve has gone from being flat to upward sloping, it means the shorter term interest rates have gone down. Recall that Macaulay duration is the PV of the payments received on a bond over its life weighted by the year each payment is received in. Also remember that a bond's current price is nothing but the summation of the different PVs of its various payments. It effectively gives the real average life of the bond - for example if a hypothetical (and impossible) bond derives half of its value from a payment today and the other half from a payment in 10 years, the investor can look at the average as being 5 years (0*50% + 10*50%). That is what is what we are calculating when deriving Macaulay duration.

In this case, a reduction in the near term interest rates increases the PV of the payments received prior to the payment at 10 years. This increases the value of the bond, and also increases the weightage of the earlier payments, decreasing the Macaulay duration (by shifting it closer to now and further behind from the maturity date).

The highest possible transformation line, ie the transformation line with the maximum slope, is the transformation line joining the risk free rate on the y-axis and the portfolio with the maximum Sharpe ratio on the efficient frontier. This line is called the 'capital markets line'. Investors can pick any point on this line according to their risk appetite, and doing so would maximize the return they can obtain for their desired level of risk. The capital markets line is tangential to the efficient frontier. The Sharpe ratio stays constant throughout the CML. Therefore statement IV is not true, while the rest are.

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.

Convenience yield is the benefit from having access to the commodity - and if the convenience yield is very high, for example in a market where manufacturers must never run out of a particular raw material, then these can switch the total cost of carry (which include interest and storage costs, less convenience yields) to being negative. This causes forward prices to become lower than spot prices, a phenomenon known as backwardation.

Therefore Choice 'b' is the correct answer. If convenience yields are less than other carrying costs, then backwardation will not happen. The sign of convenience yields does not matter, what matters is their relative magnitude when compared to the other costs of carry.

To understand this in an intuitive way, consider that forward prices are nothing but spot prices, plus interest, plus storage costs, less convenience yields. If interest and storage costs are less than the convenience yield, the market will be backwarded.

Explanation:

Remember how exchange rates are generally quoted. Most exchange rates are quoted in terms of how many foreign currencies does USD 1 buy. Therefore, a rate of 99 for the JPY means that USD 1 is equal to JPY 99. These are called 'direct rates'. However, there are four major world currencies where the rate quote convention is the other way round - these are EUR, GBP, AUD and NZD. For these currencies, the FX quote implies how many US dollars can one unit of these currencies buy. So a quote of "1.1023" for the Euro means EUR 1 is equal to USD 1.1023 and not the other way round.

Futures contracts carry no gamma. Only options have gamma. Choice 'a' is the correct answer. Any instrument whose price varies in a linear fashion with respect to the underlying will have gamma equal to zero.

The swap can be valued by valuing the two individual components of the swap.

The fixed rate bond equivalent in the swap is valued at =4/1.05 + 104/(1.06^2) = $96,369,154.

The FRN component will be valued at par as we are at a point where the rate has just been reset, ie $100m.

The investor is paying the fixed rate, and is therefore short the bond. He/she is receiving LIBOR, and is therefore long the FRN. The value of the swap to the investor therefore is +$100,000,000-$96,369,154 = $3,630,846

Detailed explanation:

An Interest Rate Swap exchanges fixed interest flows for floating rate flows. The floating rate leg is tied to some reference rate, such as LIBOR. The parties exchange net cash flows periodically. Conceptually, an interest rate swap is the combination of a fixed coupon bond and a floating rate note. The party receiving the fixed rate is long the fixed coupon bond and short the FRN, and the party receiving the floating rate is long the FRN and short the fixed coupon bond.

An interest rate swap can be valued as the difference between the two hypothetical bonds. FRNs sell for par at issue time as they pay whatever the current rate is, subject to periodic resets. Therefore immediately after a payment is made on a swap, the value of the FRN component is equal to its par value. The bond can be valued by discounting its cash flows. The difference between the two represents the value of the swap. When the swap is entered into, the fixed rate leg is set in such a way that the value of the hypothetical bond is equal to that of the FRN, and therefore the swap is valued at zero. The rate at which the fixed rate leg is set is called the swap rate. Over its life, market rates change and the value of the fixed coupon bond equivalent in our swap diverges from par (whereas the FRN stays at par - at least right after payments are exchanged and the new floating rate is set for the next period). Thus the swap acquires a non-zero value.

There are two ways to value a swap. If interest rates for the future are known, the bond and the FRN can be valued and their difference will be equal to the value of the swap. Sometimes, the current swap rates are known. In such a case, the swap can be valued by imagining entering into an opposite swap at the new swap rate, which will leave a residual fixed cash flow for the remaining life of the swap. This residual cash flow can be valued and that represents the value of the swap. For example, if a 4 year swap was entered into exchanging an annual fixed 5% payment on a notional of $100m for a floating payment equal to LIBOR, and at the end of year 1 the swap rate is 6%, then the party paying fixed can choose to enter into a new swap to receive 6% and pay LIBOR. All cash flows between the old and the new swap will offset each other except a net receipt of 1% for the next 3 years. This cash flow can be valued using the current yield curve and represents the value of the swap.

Swaps rates are calculated such that the swap's value at inception is zero. Therefore statement I is correct and statement II is incorrect. OTC swaps are not standardized, in fact they are customized by the parties to suit their needs, which is why they are over-the-counter. Therefore statement III is incorrect. It is correct that interest rate and commodity swaps are the most traded, and statement IV is correct.

Therefore Choice 'c' is the correct answer.

A fixed for floating interest rate swap would be the most appropriate to the company's needs. It will allow it to receive a fixed rate (which will offset the fixed payment it has to make on the loan) and pay a floating rate which it expects will be lower than the fixed rates. Choice 'a' is the correct answer.

Answer:

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.

A high beta does not necessarily imply a high correlation with the market. The relationship

between beta and correlation can be expressed as 103.04.e2103.04.e2, where x is the market portfolio and y is the asset under consideration.

103.04.e

This means that a high market beta could be due to high volatility of the asset in question, and not because of a high correlation. Therefore statement I is not correct.Statement II is correct as correlation and covariance have the same sign. This is because correlation = covariance/product of standard deviations. Since standard deviation is always positive, correlation and covariance will have the same sign.A correlation of zero indicates the absence of a linear relationship between two variables - therefore statement III is correct.Statement IV is correct as well, because unless correlation is +1, diversification always reduces total portfolio risk.

This question is based upon a weather derivative contract traded on the CME in the US. For each day, 'Heating-Degree-Days' (HDD) is calculated as equal to 65 degrees Fahrenheit minus the daily average temperature. The daily average temperature is based upon the temperature reported by the Earth Satellite Corporation using a specified automated weather station. Based upon daily values of HDD, an aggregated number called the 'CME degree days index' is calculated for each contract month. In other words, the index for a particular month is just the aggregation of the 'HDD' value for each of the days of that month. Each contract settles at the end of the month at a value equal to $20 x Degree Days Index. (In a similar way, 'Cooling Degree Days' are also calculated and a futures contract offered, except that CDD is equal to the average daily temperature minus 65 degrees). (Source: CME's website at CMEGroup.com)

In the given question, we are interested in hedging against the possibility of the temperature being too low. This means we should buy the HDD futures contract (the lower the temperature, the higher the difference of the average temperature from 65 degrees, and the higher the settlement). Therefore Choice 'b' is the correct answer. The lower the actual temperature turns out to be, the higher the payout to the grower. It would not be wise to wait till January to buy the contract as by then the prices of the contract would have already risen if the grower's fears of a colder January appear to be coming true. He can hedge his exposure by immediately locking in the January 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

Choice 'd' is the correct answer. Continuously compounded returns are given by the log of S2/S1. The expression (S2 - S1)/S1 gives discrete returns, not continuously compounded returns.

Note that the question is only asking for the return over the given time period, not annualized returns. So t is not relevant here. If we had to find annualized returns, and t were expressed in years, then the annualized return would have been (1/t)*ln(S2/S1).

Also refer to the tutorial on interest rates and compounding for more information on continuously compounded rates.

The TED spread is a bet on the spread between treasury bill futures and Eurodollar futures. T-bill rates are lower than Eurodollar rates, as the former carries no risk. Eurodollars deposits, which are interbank deposits between the highest rated banks, carry very little risk as well. Therefore both these instruments generally trade at very narrow spreads. The spread widens, ie the Eurodollar rates rise in comparison to treasury bill rates when the market has credit risk fears.

A trader is said to be 'long' the spread when he benefits from the spread increasing, and 'short' the TED spread when he gains from the spread decreasing. A trader can buy the spread by being long t-bill futures and short Eurodollar futures. Similarly he can be short the spread by being short t-bill futures and long Eurodollar futures.

The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity . Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06

Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73

Therefore the total value of the bond today is $95.79

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.

The riskiest tranche of a structured product is called the equity tranche. All other choices are incorrect.

The basis point value is equal to $102 x 5 /10000 = $0.051. Therefore Choice 'd' is the correct answer.

The basis point value, also called the PV01, is the dollar value change in the price of a bond as a result of a 1 basis point (=1/10000) change in interest rates. Since the modified duration is 5, it means a 1% change in interest rates produces a 5% change in the price of the bond, and a 1 bps change will therefore produce a 0.05% change in the value of the bond. Since the bond is currently valued at $102, the change works out to $102 x 0.05% = $0.051.

T-bill futures and fed futures are very short term futures contracts, and unlikely to provide much of a hedge against a rise in interest rates. FRAs however are customized and would be the right instrument for the borrower to hedge his interest rate risk. A long FRA position gives him the right to borrow at an agreed rate in the future. This rate will not change regardless of the changes in interest rates, and therefore Choice 'b' is the correct answer.

All the statements given are true, except that standard deviations cannot be averaged to get the portfolio standard deviation unless the assets are perfectly positively correlated. Therefore Choice 'd' is the false statement, and the correct answer.

For a portfolio of uncorrelated assets, ie correlations being equal to zero, variances can be added together to get portfolio variance. Also, regardless of correlations, portfolio returns are always the weighted average of asset returns, and just averages will do in this case as the portfolio is said to be equally weighted across the assets. A correlation of zero produces a risk level less than that possible with positive correlations.

Explanation:

The weighted average cost of capital (WACC) is given by the average cost of debt and equity, weighted by their proportions in the capital structure. The cost of debt should be considered after taxes, as interest is a tax deductible expense. Therefore the WACC in this case can be calculated as = [10% x (1-25%) x 0.5] + [14% x 0.5] = 10.75%

When hedging one fixed income security with another, the question as to how much of the hedge to buy (or sell) (ie the hedge ratio) for a given primary position is determined by their respective basis point values, which in turn are determined by their duration. Therefore, when hedging a long maturity bond with a PV01 of $3 with a short maturity bond that has a PV of $1, we will need to buy 3 times the notional value of the short maturity bond to achieve the same sensitivity to interest rates as the longer maturity bond. Additionally, we may also expect the interest rates on the hedge to move differently from the interest rates on the primary instrument being hedged, and this needs to be accounted for as well as part of the hedge ratio calculation. This is called the yield beta and is calculated as change in yield for primary position/change in yield for the hedge security.

The hedge ratio is determined both by the yield beta and the BPVs of the two securities.

In this case, the yield beta is 1 (as the question speaks of a parallel shift in the yield curve, ie all rates rise or fall together), and the ratio of the BPVs is 5/8. Therefore she should sell 5/8 x 1,000,000 = $625,000 of the 30 year bond.

Choice 'b' is the correct answer.

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

Generally, it is not a good idea to exercise an option early as any more upside in the remaining period to expiry is being sacrificed. However, if an extraordinarily large dividend is coming due, and this dividend is larger than the interest foregone from holding the option, it may be a good idea to exercise the option early. In such cases, the exercise needs to happen before the ex-dividend date and not afterwards. Choice 'b' is therefore the correct answer.

Even if the option is deep in the money and delta is approaching 1, and exercise upon maturity is almost a certainty, it would still always be better to sell the option than exercise it . Therefore Choice 'a' is incorrect. Choice 'c' is correct in all cases except when a large dividend is coming in. Choice 'd' is not correct because an early exercise needs to happen prior to the ex-dividend date and not afterwards.

On-the-run bonds yield less, and therefore are priced higher than similar off-the-run bonds. The difference in their pricing reflects the fact that on-the-run bonds are more liquid than off-the-run bonds. Therefore statements I and II are correct. Bonds are on-the-run when they are issued, and change hands frequently, and over time as they become 'seasoned', newer bonds take their place as on-the-run bonds making them off-the-run.

Strips are zero coupon instruments, and do not carry any coupon. Therefore statement III is not correct.

A lower bid-ask or bid-offer spread indicates lower transaction costs and is a result of greater liquidity. A higher bid-ask spread results for less liquid securities. Therefore statement IV is not correct.

The investor's needs to sell futures contracts, as his current position is long. He needs to sell ($1,000,000 x (2.5-1)) / ($240,000 x 1.2) = 5.2 contracts, or rounded to 5 contracts.

It is important to note here that the investor wishes to retain a beta of 1, and does not want to get rid of all market exposure.

The profit potential from the conversion of convertible bonds into stock is limited by the issuer's option to call the security at short notice. Generally, the convertible debt security is convertible into a certain number of shares, and the debt holder will generally not convert the security to shares unless there is a profit to be made. The 'premium' is irrelevant, because as long as the premium exists, the debt holder has no incentive to convert, as he would be better off buying the shares in the market. It is only when share prices go beyond a level that it becomes advantageous convert the security into shares. However, the prospect of granting cheap shares to the debt holders is not too appealing to the issuer, and as soon as the share price goes beyond a point where the value of the shares exceeds the face value of the debt the issuer has an incentive to exercise its option to call the security.

Therefore the profit potential from the conversion of convertible bonds into shares is limited by the issuer's option to call the security, and Choice 'a' is the correct answer. The 'premium', or interest rates, or volatility are irrelevant.

A hedge based on portfolio duration alone makes the assumption that the price/yield relationship is linear, and ignores the convexity or non-linearity of the price/yield relationship. As prices change beyond small changes, the non-linear effect kicks in, which can be offset by making a convexity adjustment to the hedge. Therefore statements I and II are correct.

Statement III is incorrect - negative convexity has an adverse effect on bond prices regardless of whether prices rise or fall.

Statement IV is correct, a bond hedge based on duration alone may be mismatched along the yield curve (eg, hedging a 10 year maturity bond with a 3 year futures contract, even though of identical total durations), which is based upon the implicit assumption that all rates will move together (ie parallel shifts).

Eurodollar deposits refer to US dollar denominated deposits outside the US, for example in a banking center such as London, and held by a non-US bank or a foreign branch of a US bank. Choice 'b' is the correct answer.

Commodity futures prices can be expressed as the summation of their spot prices and the carrying costs. Therefore any changes in either of these two would be a risk to the futures prices, and Choice 'b' is the correct answer. It is common to decompose complex commodity portfolios into underlying equivalent spot positions and the carrying costs, which includes interest, convenience yield and storage costs. For liquid commodities such as gold where changes of a short squeeze are low, interest costs dominate the carryings costs. Choice 'b' is the correct answer as it is most complete and covers the elements in the other choices. The 'lease rate' for a commodity is equivalent to (Fwd Price - Spot Price)/Spot Price, and comprises the interest and storage costs and the convenience yield. The other choices do not represent complete answers.

Since the stock is selling for $100 spot, its 3 month forward price for you would be $100*(1 + 6%*3/12) = $101.50. Since the forward is priced at $104, it is 'rich' compared to the spot and should be sold. A profitable trade would be to buy the spot and sell the forward.

Imagine you borrow $100 and buy the stock, and simultaneously sell the forward. At the end of 3 months, you will receive $104 in return from the forward, and be obliged to return the initial $100 borrowed together with interest of $1.50 for the three months. You would make a riskless profit of $2.50 per share in three months. Thus Choice 'c' is the correct answer.

Note that the treasury yield is irrelevant, what matters is the rate at which you can finance the trade which is 6% per annum.