(Global edition) John C. Hull - Options, Futures, and Other Derivatives - Solutions Manual-Pearson (2021)

[Virtual Presenter] The introduction to investing in the share market can be complex and overwhelming. Understanding the two strategies of investing, options and futures, is a crucial step in making informed decisions in the market. In this chapter, you will learn about the concept behind options and futures and how they can be used to make a profit. This includes understanding how a call option gives a payoff of max(0,T-K) and a put option gives a payoff of max(0,K-T). We will also discuss how selling a call option involves giving someone else the right to buy an asset from you and how buying a put option involves buying an option from someone else. Both of these strategies have potential payoffs of T-K. Additionally, we will explore a few short concept questions and practice questions to understand the concepts better..

[Audio] The second strategy presents a higher potential for gain and a higher potential for loss due to the leverage offered by the option. Put options are a financial derivative which allow you to speculate on a decrease in the value of an asset, while limiting your own losses should the asset price rise. As an example, if you purchase 50 contracts (each at 100 shares) with a strike price of $25 and an expiration date in four months, you will benefit should the underlying asset price decline before expiration. If the prices rises however, you are not rewarded and the money you invested in the option is lost. This leverage provides both gain and risk mitigation opportunities for your investment..

1.10 The seller of the option will lose money if the price of the stock is below $56.00 in June. (This ignores the time value of money.) The option will be exercised if the price of the stock is below $60.00 in June. The profit as a function of the stock price is shown in Figure S1.2. Figure S1.2: Profit from short position in Problem 1.10 1.11 The trader has an inflow of $2 in May and an outflow of $5 in September. The $2 is the cash received from the sale of the option. The $5 is the result of the option being exercised. The trader has to buy the stock for $25 in September and sell it to the purchaser of the option for $20. 1.12 The trader makes a gain if the price of the stock is above $26 at the time of exercise. (This ignores the time value of money.) 1.13 A long position in a four-month put option on the foreign currency can provide insurance against the exchange rate falling below the strike price. It ensures that the foreign currency can be sold for at least the strike price. 1.14 The company could enter into a long forward contract to buy 1 million Canadian dollars in six months. This would have the effect of locking in an exchange rate equal to the current forward exchange rate. Alternatively, the company could buy a call option giving it the right (but not the obligation) to purchase 1 million Canadian dollars at a certain exchange rate in six months. This would provide insurance against a strong Canadian dollar in six months while still allowing the company to benefit from a weak Canadian dollar at that time. 1.15 a) The trader sells 100 million yen for $0.0090 per yen when the exchange rate is $0.0084 per yen. The gain is 100 0 0006   millions of dollars or $60,000. b) The trader sells 100 million yen for $0.0090 per yen when the exchange rate is $0.0101.

per yen. The loss is 100 0 0011   millions of dollars or $110,000. 1.16 Most investors will use the contract because they want to do one of the following: a) Hedge an exposure to long-term interest rates. b) Speculate on the future direction of long-term interest rates. c) Arbitrage between the spot and futures markets for Treasury bonds. This contract is discussed in Chapter 6. 1.17 The statement means that the gain (loss) to one side equals the loss (gain) to the other side. In aggregate, the net gain to the two parties is zero. 1.18 The terminal value of the long forward contract is: 0 TS F where T S is the price of the asset at maturity and 0 F is the delivery price (which is the same as the forward price of the asset at the time the portfolio is set up). The terminal value of the put option is: max ( 0 T 0) F  S  The terminal value of the portfolio is therefore, 0 max( 0 0) T T S F F S     ) ,0 max( ST  F0  This is the same as the terminal value of a European call option with the same maturity as the forward contract and a strike price equal to 0 F . This result is illustrated in Figure S1.3. The profit equals the terminal value of the call option less the amount paid for the put option. (It does not cost anything to enter into the forward contract.) Figure S1.3: Profit from portfolio in Problem 1.18 1.19 Suppose that the yen exchange rate (yen per dollar) at maturity of the ICON is T S . The payoff.

[Audio] An ICON is a financial instrument that offers a combination of regular bond return and call options. The bond component guarantees a return while the call options provide additional return if the underlying asset performs well. ICONs are structured to buy 169000 yen if the forward price of the underlying asset is 1/169 and buy 84.5 yen if the forward price of the underlying asset is 1/84.5. The payoff from the ICON can be written in terms of the terminal value of the various components of the position. For example, if the terminal value of the underlying asset is ST on January 1, 2022, then the value of the first contract will be 1000 plus 169000/ST if the value of the underlying asset is below the exercise price, and 1000 plus 2000 minus 169000/ST if the value of the underlying asset is higher than the exercise price. This implies that the payoff from an ICON is greater than the payoff from a regular bond alone, as it offers the additional return from the call options..

[Audio] No matter the situation, the put option has a maximum profit of 1.29 - ST or 0 - 0.02. The profit from the long forward contract is ST - 1.2556. Combining the two, the overall profit is the maximum of 1.29 - ST - 0.02 plus ST - 1.2556. When ST is greater than 1.29, the profit is ST - 1.2756, while when ST is smaller the profit is 0.0144. Therefore, the profit from this strategy is always positive even when the time value of money is omitted..

[Audio] Option strategies such as the put option offer a lower initial cost than buying stock, with the potential to generate a higher total gain. Leveraging funds, investors can control a greater number of shares at a lower cost than purchasing the stock itself. Futures contracts make it possible to trade on the movement of a stock without taking ownership of it, while allowing traders to hedge their exposure. Additionally, traders can take advantage of arbitrage opportunities to capitalize on price discrepancies in two markets, potentially making a profit of ST-1000 or max (ST-1000, 0)-100, depending on the asset's price in a year. Utilized correctly, these strategies can generate a significant return..

1.29 The company could enter into a forward contract obligating it to buy 3 million euros in three months for a fixed price (the forward price). The forward price will be close to but not exactly the same as the current spot price of 1.1500. An alternative would be to buy a call option giving the company the right but not the obligation to buy 3 million euros for a particular exchange rate (the strike price) in three months. The use of a forward contract locks in, at no cost, the exchange rate that will apply in three months. The use of a call option provides, at a cost, insurance against the exchange rate being higher than the strike price. 1.30 (Excel file) This is known as a bull spread (see Chapter 12). The profit is shown in Figure S1.5. Figure S1.5: Profit in Problem 1.30 1.31 The arbitrageur should borrow money to buy a certain number of ounces of gold today and short forward contracts on the same number of ounces of gold for delivery in one year. This means that gold is purchased for $1,200 per ounce and sold for $1,300 per ounce. Interest on the borrowed funds will be 0.03×$1,200 or $36 per ounce. A profit of $64 per ounce will therefore be made. 1.32 The second alternative involves what is known as a stop or stop-loss order. It costs nothing and ensures that $29,000, or close to $29,000, is realized for the holding in the event the stock price ever falls to $290. The put option costs $2,130 and guarantees that the holding can be sold for $29,000 any time up to December. If the stock price falls marginally below $290 and then rises the option will not be exercised, but the stop-loss order will lead to the holding being liquidated. There are some circumstances where the put option alternative leads to a better outcome and some circumstances where the stop-loss order leads to a better outcome. If the stock price ends up below $290, the stop-loss order alternative leads to a better outcome because the cost of the option is avoided. If the stock price falls to $280 in November and then rises to $350 by December, the put option alternative leads to a better outcome. The investor is paying $2,130 for the chance to benefit from this second type of outcome. 1.33 Suppose T S is the price of oil at the bond’s maturity. In addition to $1,000, the Standard Oil bond pays:.

[Audio] An investor can structure a bull spread in oil by taking advantage of the price differences between two different options. This would include a long position in 170 call options on oil with a strike price of $25 and a short position in 170 call options on oil with a strike price of $40, which is outlined in Chapter 12 of a book. Another way to help mitigate risk using options is through a range forward contract. This would involve selling a put option on GBP with a strike price of 1.19 and buying from the treasurer a call option on GBP with a strike price of 1.25, covering one million pounds and having a six-month maturity. This is further discussed in Chapter 17..

[Audio] Futures markets and central counterparties are a key topic in this chapter. Margin calls are triggered when loss of a certain amount of money is recorded in the margin account. To illustrate this, let's say that the price of silver goes up by $0.20 to $17.40 per ounce. This results in a total profit of $2,200 between September 2021 and December 2021 and an additional $1,400 between January 1st, 2022 and March 2022. Hedgers will be taxed on the entirety of the profit in 2022, whereas speculators will have to split the amount between 2021 and 2022. Additionally, stop and limit orders are useful for limiting losses or taking advantage of various price points. Futures markets also provide various pricing options depending on the currency involved. This affects the attractiveness of the contract for both parties and should thus be taken into account when trading..

[Audio] Margin system is an advantageous tool for investors as it requires them to deposit more funds to cover losses if they occur. Market-if-touched and stop orders are two methods used to manage exposure to the market and protect profits or limit losses. Furthermore, arbitrage opportunities arise when the futures price is higher than the spot price during the delivery period. This enables an investor to buy the underlying asset, sell a futures contract and capitalize on the difference. Yet, when the futures price is lower than the spot price, no perfect arbitrage strategy exists and timing when delivery can be made comes into play. Companies may benefit from entering into a long futures contract and waiting for delivery..

[Audio] Regulations mandating most standard over-the-counter (OTC) transactions between financial institutions to be cleared by central clearing counterparties dictate obligations for initial and variation margin requirements similar to exchanges. Although such requirements augment collateral, netting of transactions with different counterparties diminish the total impact. Examining the 1.1000 forward quote and 0.9000 futures quote of the Swiss franc reveals that the forward market is much more attractive for a trader attempting to sell Swiss francs. When trading live hog futures, the broker will ask for initial margin and subsequently pass on the order to a commission broker for execution according to instructions. Speculators also have an integral function by providing liquidity in the market..

[Audio] Open interest refers to the total number of contracts outstanding between all participating entities. A new contract increases the open interest by one, while closing out or offsetting an existing position reduces it by one. Profit is calculated by subtracting the opening price from the closing price. Futures contracts offer investors a tool to hedge their exposure to an asset while speculating on its price. For instance, a farmer may use futures contracts to counter potential losses due to price changes, while a mining company may be able to secure the price of its gold production by shorting futures contracts. A central counterparty (CCP) is similar to a clearing house in exchange-traded contracts and plays the role of the third party in an over-the-counter (OTC) derivative transaction, taking responsibility for the credit risk and requiring initial and variation margin..

[Audio] Trader A and Trader B both invested in the share market with different approaches. Trader A chose to use options, which give them built-in leverage, while Trader B chose to use futures contracts, speculating with investments that are hedged against exposure to assets. After three months, each trader had successfully gained profits in the market. Trader B's profits were realized at the end of the three months, while Trader A's profits were realized day-by-day during the period. The open interest of the contract went down by 600, suggesting that 1,400 shorts were closed out and 800 new shorts were taken, as well as 1,200 longs closed out and 600 new longs. Additionally, if the price of wheat futures rises by 20 cents, there is a margin call of $1000. Furthermore, there is a potential profit of $5 per barrel when going long on one June oil contract and short on one December contract. The payoff of long forward contract is ST - K and the payoff of short forward contract is K - ST, both depend on the spot price..

[Audio] Collateral can be a useful tool when executing a hedge, but it carries the potential for a net loss. In this case, the bank has offered $3 million as collateral, expecting to make a gain when the futures contract expires. However, if the trade does not go as anticipated, the bank will incur a net loss of $3 million..

[Audio] For an optimal hedge, the hedge ratio should be 0.652, meaning that the size of the futures position should be 64.2% of the size of the company's exposure. This means that 88.9 contracts should be shorted and, to reduce the beta to 0.6, a short position in 44 contracts is required. It is recommended to select a futures contract that has a delivery month as close as possible to, but later than, the month containing the expiration of the hedge..

[Audio] Hedging risk in foreign exchange can be done through the use of forward and futures contracts. A forward contract locks in the forward exchange rate, which may be different from the spot exchange rate. The basis, the difference between the spot and futures prices, may also play a part. To determine how much hedging is needed, it is important to estimate cash flows in foreign currency. Additionally, companies should consider how exchange rate changes could impact profits in foreign markets. Depending on their assessment, businesses can decide if futures and options are the best strategies to reduce their risk. Hedging does not always guarantee increased profits, but it can help manage risk and reduce downside associated with foreign exchange movements..

[Audio] According to the 3rd Fundamental Theorem of Asset Pricing, the optimal hedge ratio is calculated from the covariance of the asset and the variance of the futures contract. This ratio is commonly referred to as the minimum variance hedge ratio and can help individuals and companies protect themselves against risks associated with assets while simultaneously engaging in speculation with futures contracts. For example, a company may use the optimal hedge ratio to secure a price close to the futures price when it knows it will purchase a certain commodity in the future. This is particularly profitable if the futures price is lower than the spot price. However, when there is a high degree of uncertainty, for example due to weather conditions, caution should be exercised when entering into short forward contracts. Losses from the short futures position could worsen any problems that arise from unpredictable occurrences. Therefore, one should always take into account the entire context when deciding whether to hedge or not..

[Audio] This slide explains two strategies for investing in the share market – options and futures contracts – and how they can be used to leverage profits and hedge against risks. An example of the former is how Goldman Sachs can borrow 1 ounce of gold and sell it for $1200, agreeing to buy the gold back at a lower price in one year in order to make a profit. As for the latter, if a trader is seeking to hedge their exposure to an asset, they can use a hedge ratio of 1 to be $0.85 per barrel better off than if they were to use a futures contract only for speculation. For instance, if the spot price of light sweet crude is higher than the futures price at the time the hedge is closed out, the excess of the spot over the futures would be $0.20 per ounce and the trader would have to short five contracts to reduce risks..

[Audio] The hedge ratio of 0.9 and the corresponding number of contracts are calculated from equation 3.1. A portfolio with a beta of 0.2 and a decrease of 30% in the market return has an expected return of -2%. If the actual return is -10%, the portfolio manager has done 8% worse than the simple index portfolio. To hedge the portfolio, the company should short 140 contracts and take a long position of 60 contracts, calculated by 250000*2.1(-5.0)+100000000 and 250000*2.1(2.1)+100000000 respectively..

[Audio] Investments with annual compounding have a rate of return of 10% per annum, while semi-annual compounding has a return of 5.488% per annum. To calculate the bond price, cash flows should be discounted at 5.2% over 18-months, with a zero rate of 5.204%. By using these strategies, investors can increase their exposure to assets and speculate with futures contracts..

[Audio] The compounding frequency has an impact on the return on investment. If, for example, the rate of return is 10%, the effective annual return will change, leaning higher for a higher compounding frequency. Quarterly compounding, for example, produces an annual return of 9.76%, comparably lower than the 9.57% from monthly compounding, or the 9.53% from continuous compounding. The forward rate for every quarter forecasts the return rate over the subsequent quarter. An upward sloping yield curve shows the short term rate below the long term rate. On the other hand, when the yield curve slopes downwards, the opposite is true. Duration reveals the effects of a small parallel shift on the yield curve, and the value of a bond portfolio. The decrease in the value of the portfolio is similar to the duration of the portfolio multiplied by the extent to which interest rates have risen. However, duration has limits and only applies to parallel shifts in the yield curve..

[Audio] The rate of interest with quarterly compounding is 7.97% per annum and the amount of interest paid each quarter is $100.50. For the first two bonds, the cash price is $98.04 and the bond yields are 6.407% and 7.741% respectively. The first bond pays $2 in 6, 12, 18 and 24 months and $102 in 30 months. The second bond pays $4 in 6, 12, 18, 24 and 30 months and $104 in 36 months..

[Audio] Two bonds with different coupon rates can lead to cash flows that balance each other out. The liquidity preference theory states that long term rates are higher than expected future short term rates, resulting in an upward sloping yield curve more often than downward sloping. Par yield is different from zero rate, with the yield on a coupon bearing bond being lower than a zero coupon bond when the yield curve is upward sloping..

[Audio] Bond yield is a quantification of the amount of return on investment generated by holding a particular bond. When the yield decreases, the price of the bond increases. As an example, if the yield of a certain bond is 6.8%, its price will be 103.95. A 6 month Treasury bill results in a rate of return of 6.383% over six months, which is equivalent to annual returns of 12.766% with semiannual compounding or 12.38% if continuously compounded. The rate of return for a 12 month Treasury bill is 11.89% with annual compounding or 11.65% if continuously compounded. The zero rate for a 1.5 year bond is 11.5%, and for a 2-year bond is 11.3%..

[Audio] We analyze the answer of the question posed in Excel file 4.23, which is 4.07%. Comparing different compounding systems, we assess the effect of a 10 basis points increase in yields. After analyzing the results, we conclude that the percentage changes in the values of the two portfolios for a 10 basis point increase in yields are the same, and portfolio A has greater convexity than portfolio B when yields increase by 5%..

[Audio] We calculate a bond duration by deriving the DV01 and bond price change for a bond with a principal value of 100, a life of 2 years, and a coupon rate of 6%, payable semi-annually. Using yield curve data from Table 4.2, the bond price is calculated to be 98.38506. The DV01 is worked out by averaging the impact of a one basis-point increase and a one basis-point decrease. When the term structure rate is raised to 5.01, 5.81, 6.41, and 6.81, the bond price decreases to 98.36625, corresponding to the DV01. The effect on price predicted by the DV01 is 200 x −0.01881 or −3.7638. When increasing all rates by 2%, the bond price reduces to 94.694. The gamma is 0.036931 per % per %, and the convexity correction gamma is 0.5 x 0.036931 x 22 = 0.0739. Combining the DV01 and gamma, the estimated price change is 3.690 which is very close to the actual change..

CHAPTER 5 Determination of Forward and Futures Prices Practice Questions 5.1 The forward price of an asset today is the price at which you would agree to buy or sell the asset at a future time. The value of a forward contract is zero when you first enter into it. As time passes, the underlying asset price changes and the value of the contract may become positive or negative. 5.2 The forward price is 30e0.05×0.5 = 30.76. 5.3 The futures price is 350e(0.04-0.03)×0.3333 = 351.17. 5.4 Gold is an investment asset. If the futures price is too high, investors will find it profitable to increase their holdings of gold and short futures contracts. If the futures price is too low, they will find it profitable to decrease their holdings of gold and go long in the futures market. Copper is a consumption asset. If the futures price is too high, a strategy of buy copper and short futures works. However, because investors do not in general hold the asset, the strategy of sell copper and buy futures is not available to them. There is therefore an upper bound, but no lower bound, to the futures price. 5.5 A foreign currency provides a known interest rate, but the interest is received in the foreign currency. The value in the domestic currency of the income provided by the foreign currency is therefore known as a percentage of the value of the foreign currency. This means that the income has the properties of a known yield. 56 The futures price of a stock index is always less than the expected future value of the index. This follows from Section 5.14 and the fact that the index has positive systematic risk. For an alternative argument, let  be the expected return required by investors on the index so that ( ) 0 ( ) q T E ST S e    . Because   r and ( ) 0 0 r q T F S e   , it follows that 0 ( E ST )  F . 5.7 a) The forward price, 0 F , is given by equation (5.1) as: F0 = 40e0.05×1 = 42.05 or $42.05. The initial value of the forward contract is zero. b) The delivery price K in the contract is $42.05. The value of the contract, f , after six months is given by equation (5.5) as:.

f = 45−42.05e−0.05×0.5 = 3.99 i.e., it is $3.99. The forward price is: 45e0.05×0.5 = 46.14 or $46.14. 5.8 Using equation (5.3), the six month futures price is 150 (0 07 0 032) 0 5 152 88 e        or $152.88. 5.9 The futures contract lasts for five months. The dividend yield is 2% for three of the months and 5% for two of the months. The average dividend yield is therefore 1 (3 2 2 5) 3 2 5 %      The futures price is therefore 1300e(0.04-0.032)×0.4167=1304.34 or $1304.34. 5.10 The theoretical futures price is 400e(0.06-0.04)×4/12=402.68 The actual futures price is 405. This shows that the index futures price is too high relative to the index. The correct arbitrage strategy is the following: 1. Sell futures contracts. 2. Buy the shares underlying the index. 5.11 The settlement prices for the futures contracts are to Jun: 0.93070 Sept: 0.93200 The September price is 0.14% above the June price. This suggests that the short-term interest rate in Japan was less than the short-term interest rate in the U.S. by about 0.14% per three months or about 0.56% per year. 5.12 The theoretical futures price is 1.0500e(0.02-0.01)×2/12= 1.0518 The actual futures price is too low. This suggests that a Swiss arbitrageur should sell Swiss francs for US dollars and buy Swiss francs back in the futures market. 5.13 The present value of the storage costs for nine months are 0.06+0.06e-0.05×0.25+0.06e-0.05×0.5= 0.178 or $0.178. The futures price is from equation (5.11) given by 0 F where.

[Audio] A comparison between forward and futures contracts can be made in terms of how they can be used as a hedge. Long-term forward contracts provide a perfect hedge while long-term futures contracts provide a slightly imperfect hedge. Depending on the situation, either one can lead to a better outcome on a present value basis. Therefore, investors should factor in the timing of cash flows and the value of money when deciding between a forward and a futures contract..

[Audio] Expected future price can be understood as the average of different people's subjective opinions. To calculate this expected future price, we can take the sum of the different prices times their respective probabilities. In the case of commodity futures trading, Keynes and Hicks argued that speculators tend to make money while hedgers tend to lose money. This implies that futures prices for commodities will usually be higher than the expected future spot prices. Therefore, when futures prices decrease by 2% annually, the expected spot prices must be declining even faster..

( )( ) r rf T t t t F S e    Suppose that the hedge ratio is h . The price obtained with hedging is ( 0 t ) t h F F S   where 0 F is the initial futures price. This is ( )( ) 0 r rf T t t t hF S hS e     If ( )( ) fr r T t h e    , this reduces to 0 hF and a zero variance hedge is obtained. (b) When t is one day, h is approximately ( ) 0 0 fr r T e S F   . The appropriate hedge ratio is therefore 0 0 S F . (c) When a futures contract is used for hedging, the price movements in each day should in theory be hedged separately. This is because the daily settlement means that a futures contract is closed out and rewritten at the end of each day. From (b) the correct hedge ratio at any given time is, therefore, S F where S is the spot price and F is the futures price. Suppose there is an exposure to N units of the foreign currency and M units of the foreign currency underlie one futures contract. With a hedge ratio of 1, we should trade N M contracts. With a hedge ratio of S / F, we should trade SN FM contracts. In other words, we should calculate the number of contracts that should be traded as the dollar value of our exposure divided by the dollar value of one futures contract. (This is not the same as the dollar value of our exposure divided by the dollar value of the assets underlying one futures contract.) Since a futures contract is settled daily, we should in theory rebalance our hedge daily so that the outstanding number of futures contracts is always ( ) ( ) SN FM . This is known as tailing the hedge. (See Chapter 3.) 5.21 a) The risk-free rate, b) the excess of the risk-free rate over the dividend yield, c) the risk- free rate plus the storage cost, d) the excess of the domestic risk-free rate over the foreign risk-free rate. 5.22 The theoretical forward exchange rate is 1.0404e(0.0025−0)×0.25 = 1.041. If the actual forward exchange rate is 1.03, an arbitrageur can a) borrow X Swiss francs, b) convert the Swiss francs to 1.0404X dollars and invest the dollars for three months at 0.25%, and c) buy X Swiss francs at 1.03 in the three-month forward market. In three months, the arbitrageur has 1.0404Xe0.0025×0.25 = 1.041X dollars. A total of 1.3X dollars are used to buy the Swiss francs under the terms of the forward contract and a gain of 0.011X is made. If the actual forward exchange rate is 1.05, an arbitrageur can a) borrow X dollars, b) convert the dollars to X/1.0404 Swiss francs and invest the Swiss francs for three months at zero interest rate, and c) enter into a forward contract to sell X/1.0404 Swiss francs in three months. In three months, the arbitrageur has X/1.0404 Swiss francs. The forward contract converts these to (1.05X)/1.0404=1.0092X dollars. A total of Xe0.0025×0.25 =1.0006X is needed.

[Audio] This slide aims to demonstrate how a trader can protect their investment when speculating with futures contracts. It clarifies how a profit of 0.0086X dollars can be made when a loan is taken to buy fifty barrels of oil at a cost of 1950. This is then used to calculate the futures price for a three-month contract of 1205.41, and a six-month contract of 1215.09, both of which are dependent on an assumed six-month euro interest rate of 1.835%. The present value of the storage costs per barrel is 2.854, and an upper bound to the one-year futures price is 55.56. This information allows the trader to make informed decisions on the best leverage and hedging strategies available when speculating in the futures market..

[Audio] We reviewed the practice questions that explain how to calculate the interest earned per $100 of principal in different scenarios relating to Interest Rate Futures, which is the topic of chapter 6. Discussions included obtaining the cash price for a bond, how to calculate the gain from a 6 basis points increase, the rate of 3.0409%, the value of a contract, and the number of contracts that should be shorted. We also discussed the cash price of a Treasury bill and the annualized continously compounded return..

[Audio] It is essential to ascertain the precise amount of days that has passed between two dates. Hence, the number of days between January 27 and May 5, and January 27 and July 27, should be counted to find out the amount of interest due. Thus, the number of days is 98 and 181, respectively. The quoted price of the asset is 110.5312, and the cash price is $113.78. The cheapest-to-deliver bond is then established by assessing the ‘quoted price’, ‘futures price’ and ‘conversion factor’ of each of the four bonds, indicating that bond four is the cheapest-to-deliver..

[Audio] Bond trading arbitrage involves exploiting discrepancies between the spot and futures prices of the underlying bonds. Generally, the spot price is lower than the futures price, so the arbitrageur buys the bond while shorting the equivalent number of bond futures contracts. However, this approach is complicated by the unknown delivery bond at maturity. If the futures price is too low, the arbitrageur might not be able to gain any profit from the strategy..

[Audio] Treasury bond futures contracts can be used to hedge an exposure to assets, while speculating with futures contracts to gain offsetting gains should bond prices decrease. Depending on the day count convention used, the treasurer should short either 88 or 51 bonds, respectively, with the 30/360 or actual/actual (in period) conventions. This will reduce the duration from 7.1 to 3.0, as opposed to 7.1 to 0. Daily settlement, however, causes futures contracts to have a rate higher than forward rates. Ultimately, the amount of days between the "spot date" and the delivery date is subject to the convention used..

[Audio] The Eurodollar futures contract provides investors with the opportunity to borrow money at a rate of 2.07% and invest it in a 90-day and 180-day instrument that offers a return of 2.4%, a rate that surpasses the borrowing rate. This provides a return premium, making the Eurodollar futures contract a desirable investment option. US Eurodollar futures contracts are concluded at a specified time, giving investors the opportunity to secure a forward rate to cover the period between the contract time and three months thereafter. Through these factors, the fixed rate, principal amount, and the difference between the two times, Canadian dollar cash flows resulting from the contract can be calculated..

[Audio] A strategy of hedging using futures contracts generally involves holding a long-term and a short futures contract of equal size and duration. This ensures that any gain from one contract can offset losses from the other. In this particular case, the short futures contract is used to hedge the losses on a bond portfolio whilst the trader speculates on the market. A rise in the long-term rate will result in a gain on the short futures contract; however, if the rate drops, the same holds true for the trader's loss on the short futures contract. Nevertheless, the trader should still benefit from reduced losses on the bond portfolio..

[Audio] Company X and Company Y both have apparent comparative advantages in different markets, fixed and floating rate respectively, but wish to borrow in the opposite market. A swap provides a solution that creates a gain for all parties, with the bank taking a 0.1% cut of the gain, leaving total gain of 1.4% and 0.4% per annum, respectively, for Company X and Company Y. Through this arrangement, Company X will have access to SOFR at 0.3%, and Company Y to 6.0%. Question 7.1 outlines the basis for this swap, Question 7.2 considers the party paying floating, and gives a value for the swap of $1.2817, and Question 7.3 gives an example of how this swap could be used by Company X and Company Y in the context of their comparative advantages..

[Audio] A swap for Problem 7.3 involves two parties agreeing to exchange interest payments on a specified amount of money in different currencies. One party will pay 6.536% per annum in Yen, while the other party will pay 3.922% per annum in US Dollars. The value of the swap to the party paying in sterling is obtained by subtracting the value of a sterling bond from the value of a dollar bond with the same principal amount, resulting in a value of -2.321 million dollars. The value of the swap can also be calculated by viewing it as a portfolio of forward contracts, with the result being the same -2.321 million dollars..

[Audio] LIBOR minus 0.2% of $10 million). The financial institution would be able to buy back its note for $35000. This would result in an interest rate of 5.7% per annum for the three years to the financial institution. The swap between Companies X and Y enables each party to benefit from a spread of 0.8% per annum. Company X will earn a fixed-rate return of 8.3% per annum while Company Y will earn LIBOR plus 0.3%. The financial institution will earn 0.2% from the swap while both parties will benefit from an overall return of 0.8%. At the end of year 3, the financial institution will receive $200000 and pay $150000. By buying back its note for $35000, the financial institution will be able to secure an interest rate of 5.7% per annum for the three years..

[Audio] Calculating the cost of a swap in the event of a default can be complex. For example, our equation is F= (1 + r/f)T - 1, where F is the T-year forward rate, r is the domestic risk-free rate and f is the foreign risk-free rate. In this case, r is 0.08 and f is 0.03, leading to spot and one to four-year forward exchange rates at the end of year 6. The cash flows lost due to default are then calculated, and discounted to the end of year 6 at 8% per annum, resulting in a cost of default of 679,800 dollars. Although complex, this calculation is a necessary step in determining the ultimate cost of a swap in the event of a default..

[Audio] The strategies for investing in the share market include leveraging options and hedging assets with futures contracts. Companies A and B both have offsetting plain vanilla interest rate swaps with a financial institution, with Company A paying a floating rate of US$+1%, and Company B paying C$5%. Figure S7.4 displays the net cash flow for the financial institution from these two trades. The principal payments flow oppositely at the beginning and the same direction at the end of the life of the swap. The financial institution is exposed to foreign exchange risk, which could be managed by using forward contracts. The Australian dollar bought in Year 2 is more economical than in Year 1, and the spread is always above 20 basis points..

[Audio] An interest rate swap is a powerful strategy to hedge financial risk. Instead of having exposure to the principal, a financial institution is exposed to the difference between a fixed and a floating rate of interest. To manage this exposure, institutions enter into interest rate swaps with other financial institutions or corporations, meaning they pay the floating rate and receive the fixed-rate. The value of the swap can be determined by calculating the difference between the two cash flows, discounted by the relevant currency rate, and adjusting for exchange rates. This example shows the value in millions of dollars to be -0.76, offering an effective way of hedging financial exposure while taking exchange rates into account..

[Audio] Currency swaps allow companies A and B to hedge their exposure to different assets while taking advantage of difference in market rates. By exchanging different currencies in different portions at different times, both companies can benefit financially. The bank is also able to benefit from this arrangement, earning a 10-basis point spread. This allows Company A to borrow at an effective rate of 6.85% per annum in US dollars, and Company B to borrow at an effective rate of 10.45% per annum in sterling. Both companies will save a total of 15 basis points, with the bank coming out 10 basis points better off. This demonstrates how options can be used for leverage and how traders can benefit from hedging their exposure to assets with futures contracts..

[Audio] The figure shows the potential for a swap where the counterpart can get 4.2% in exchange for LIBOR, which has a present value of $90,773. This is calculated by taking 4.2% that the counterparty will receive and subtracting the 4% they will pay, and multiplying this by the principal amount of $10 million, and then multiplying it by the discount factor of 0.5. They will receive these funds over five years in semi-annual payments of $10000..

[Audio] Securitization and how it affects the financial markets during times of crisis were discussed in this chapter, as well as the Financial Crisis of 2007-8 and the losses associated with different tranches of asset-backed securities and collateralized debt obligations. A set of practice questions on these topics were presented in order to gain a better understanding of the concepts. Those questions included the increase in price of houses, the securitization of subprime mortgages, investor underestimate of default correlations, and how an asset-backed security collateralized debt obligation is created from BBB-rated tranches of an ABS. Additionally, the structure of the tranches and how the number of defaults needed for a senior tranche of an ABS to be affected can be calculated were explained. These insights provide a deeper understanding of the complexity the Financial Crisis of 2007-8 has brought to the share market as a result of securitization..

8.7 As indicated in Table 8.1, a moderately high loss rate will wipe out the mezzanine tranches of ABSs so that the AAA-rated tranche of the ABS CDO is also wiped out. A moderately high loss rate will at worst wipe out only part of the AAA-rated tranche of an ABS. 8.8 The end-of-year bonus usually reflects performance during the year. This type of compensation tends to lead traders and other employees of banks to focus on their next bonus and therefore have a short-term time horizon for their decision making. 8.9 Losses to subprime portfolio Losses to Mezz tranche of ABS Losses to equity tranche of ABS CDO Losses to Mezz tranche of ABS CDO Losses to senior tranche of ABS CDO 2% 0% 0% 0% 0% 6% 6.7% 67% 0% 0% 14% 60% 100% 100% 38.5% 18% 86.7% 100% 100% 79.5% 8.10. Losses to subprime portfolio Losses to Mezz tranche of ABS Losses to equity tranche of ABS CDO Losses to Mezz tranche of ABS CDO Losses to senior tranche of ABS CDO 10% 0% 0% 0% 0% 13% 15% 100% 25% 0% 17% 35% 100% 100% 7.1% 20% 50% 100% 100% 28.6% 8.11 When the AAA-rated tranches of an ABS experiences defaults, the mezzanine tranches of the ABSs must have been wiped out. As a result, the AAA tranche of the ABS CDO has also wiped out. If the portfolios underlying the different ABSs have the same default rates, it must therefore be the case the AAA-rated tranche of the ABS is safer than the AAA-rated tranche of the ABS CDO. If there is a wide variation in the default rates, it is possible for the AAA- rated tranche of the ABS CDO to fare better than some (but not all) AAA-rated tranches of the underlying ABSs. Resecuritization can only be successful if the default rates of the underlying ABS portfolios are not highly correlated. The best approach would seem to be to obtain as much diversification as possible in the portfolio of assets underlying the ABS. Resecuritization then has no value. 8.12 For losses to be experienced on the AAA-rated tranche of the CDO squared, the loss rate on the mezzanine tranches of the ABS CDOs must be greater than 35%. This happens when the loss rate on the mezzanine tranches of ABSs is 10 + 0.35 × 25 = 18.75%. This loss rate.

[Audio] We have found that the occurrence of loss on the underlying assets is at a rate of 7.81%. We have seen how options provide built-in leverage and how traders can hedge their exposure to assets while speculating with futures contracts. We have considered different strategies for investing in the share market and discussed the associated risks. This concludes our presentation, thank you for your attention..