...money changes hands until the maturity date of the contract when delivery and receipt are typically made. A futures contract is an exchange-traded instrument with standardized features specifying contract size and delivery date. Futures contracts are marked-to-market daily to reflect changes in the settlement price. Delivery is seldom made in a futures market. Rather a reversing trade is made to close out a long or short position. 2. In order for a derivatives market to function most efficiently, two types of economic agents are needed: hedgers and speculators. Explain. Answer: Two types of market participants are necessary for the efficient operation of a derivatives market: speculators and hedgers. A speculator attempts to profit from a change in the futures price. To do this, the speculator will take a long or short position in a futures contract depending upon his expectations of future price movement. A hedger, on-the-other-hand, desires to avoid price variation by locking in a purchase price of the underlying asset through a long position in a futures contract or a sales price through a short position. In effect, the hedger passes off the risk of price variation to the speculator who is better able, or at least more willing, to bear this risk. 3. Why are most futures positions closed out through a reversing trade rather than held to delivery? Answer: In forward markets, approximately 90 percent of all contracts that...
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...reinvestment risk) may have greater price volatility than bonds with lower durations. It is an important tool in structuring and managing a fixed-income portfolio based on selected investment objectives. Investment theory tells us that the value of a fixed-income investment is the sum of all of its cash flows discounted at an interest rate that reflects the inherent investment risk. In addition, due to the time value of money, it assumes that cash flows returned earlier are worth more than cash flows returned later. In its most basic form, duration measures the weighted average of the present value of the cash flows of a fixed-income investment. All of the components of a bond—price, coupon, maturity, and interest rates—are used in the calculation of its duration. Although a bond’s price is dependent on many variables apart from duration, duration can be used to determine how the bond’s price may react to changes in interest rates. This issue brief will provide the following information: < A basic overview of bond math and the components of a bond that will affect its volatility. < The different types of duration and how they are calculated. < Why duration is an important measure when comparing individual bonds and constructing bond portfolios. < An explanation of the concept of convexity and how it is used in conjunction with the duration measure. January 2007 issue brief Basic Bond Math and Risk Measurement The price of a bond, or any fixed-income investment...
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...certificates. These savings certificates were highly affected by interest rate fluctuations. The long term loans provided to people generate interest earnings which are do not increase or decrease with the interest rate fluctuations. Therefore, there was a mismatch between the interest rates earned by the bank and the interest rates that it had to give out. This caused large losses over the period 1979-1982 when interest rates rose. Table 1.1 The bank would violate the regulatory capital requirements if its losses were not controlled. The T-bill interest rates were on the rise. $400mm in savings certificates were to be rolled over on September 1. If interest rates continued to rise, then these certificates would be rolled over at the prevalent high interest rates (as mentioned in the case, the savings certificate interest rate was fixed at a spread over the T-bill interest rate). If the firm hedges itself from the interest rate fluctuations, then the loss that would be caused due to the savings certificate rollover at a high interest rate would be offset by the futures position. Let us look at this in detail: From exhibit 3, Profit and Loss Statement, comparison of the interest payment expenses ( as denoted by Dividends) has increase from 1979 to 1981 by 104.3% which is attributed to the rise in T-bills interest rates. Table 1.2 Time Period 1981 1980 1979 % Increase from 1979 to 1981 Dividends (denotes interest paid or credited to members) 40,162 26781 19660 104.3% Net...
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...Interest Rate Risk Dr HK Pradhan XLRI Jamshedpur Hull Ch 7 Fabozzi chapters on duration & Convexity, Ch-7, Convexity Stochastic Process notes Session Objectives j Valuation of fixed income securities Risks in fixed income securities Traditional measures of risk – (we know PVBP, duration and convexity, M-Square) M Square) VaR based risk measures Interest rate volatility calculations Portfolio risk & Cash flows mapping issues Var for Interest Rate Derivatives Interest rate risk and Bond portfolio management Profile of Interest Rate Markets, Instruments & Institutions Bond Price P 1 y C1 1 1 y C2 2 1 y Ct C3 3 1 y n Cn price Sum of the present values of each cashflows p P n t 1 1 y t M 1 y n yield price < par (discount bond) price = par (par bond) price > par (premium bond) Concept of Accrued Interest p When you buy a bond between coupon dates, you pay the seller: Clean Price plus the Accrued Interest – pro-rated share of the fi coupon: i d h f h first interest d does not compound b d between coupon payment dates. LD Days Accrued Interest Total T from last Coupon between Coupon Date Dates Days ND (Coupon) Dirty Price Clean price Accrued Interest Accrued Interest Face * C T LD * 2 ND LD Bond Valuation Value of a bond is the present value of future cashflows, so...
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...Financial Mathematics for Actuaries Chapter 8 Bond Management Learning Objectives 1. Macaulay duration and modified duration 2. Duration and interest-rate sensitivity 3. Convexity 4. Some rules for duration calculation 5. Asset-liability matching and immunization strategies 6. Target-date immunization and duration matching 7. Redington immunization and full immunization 8. Cases of nonflat term structure 2 8.1 Macaulay Duration and Modified Duration • Suppose an investor purchases a n-year semiannual coupon bond for P0 at time 0 and holds it until maturity. • As the amounts of the payments she receives are different at different times, one way to summarize the horizon is to consider the weighted average of the time of the cash flows. • We use the present values of the cash flows (not their nominal values) to compute the weights. • Consider an investment that generates cash flows of amount Ct at time t = 1, · · · , n, measured in payment periods. Suppose the rate of interest is i per payment period and the initial investment is P . 3 • We denote the present value of Ct by PV(Ct ), which is given by Ct . PV(Ct ) = t (1 + i) and we have P = n X (8.1) PV(Ct ). (8.2) t=1 • Using PV(Ct ) as the factor of proportion, we define the weighted average of the time of the cash flows, denoted by D, as D = = n X t=1 n X t " PV(Ct ) P twt , # (8.3) t=1 where PV(Ct ) wt = . P 4 (8.4) P •...
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...These savings certificates were highly affected by interest rate fluctuations. The long term loans provided to people generate interest earnings which are do not increase or decrease with the interest rate fluctuations. Therefore, there was a mismatch between the interest rates earned by the bank and the interest rates that it had to give out. This caused large losses over the period 1979-1982 when interest rates rose. Table 1.1 The bank would violate the regulatory capital requirements if its losses were not controlled. The T-bill interest rates were on the rise. $400mm in savings certificates were to be rolled over on September 1. If interest rates continued to rise, then these certificates would be rolled over at the prevalent high interest rates (as mentioned in the case, the savings certificate interest rate was fixed at a spread over the T-bill interest rate). If the firm hedges itself from the interest rate fluctuations, then the loss that would be caused due to the savings certificate rollover at a high interest rate would be offset by the futures position. Let us look at this in detail: From exhibit 3, Profit and Loss Statement, comparison of the interest payment expenses ( as denoted by Dividends) has increase from 1979 to 1981 by 104.3% which is attributed to the rise in T-bills interest rates. Table 1.2 Time Period | 1981 | 1980 | 1979 | % Increase from 1979 to 1981 | Dividends (denotes interest paid or credited to members) | 40,162 |...
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...be intermediate -term bonds In the fixed-income market. Example – Investing money for buying a house in 5 years, investing in machineries which will last for 5 years. * Long Term Investments: The account on the asset side of the balance sheet of any company which represents the investments that the company intends to hold for more than ten year. It includes real estate, stocks, bonds and cash. Example – Investing money in retirement scheme benefits, investing in long term assets of factories. Measurement of duration: * Effective duration can be defined as the percentage change in security’s price that results from a change in yield of 100 basis points. e.g. - The price of a bond with an effective duration of 2 years will rise 2% for every 1% decrease in the yield. Similarly the price of a bond with duration of 5 years will rise 5% for a 1% decrease in the yield. As interest rates and bond yields are directly correlated, the longer the...
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...perform a certain action. More specifically in finance it means that if we buy a call option we have the right but not the obligation to buy: a fixed amount; at a fixed time; at a fixed price; of the underlying instrument. On the other hand if we buy a put option we have the right but not the obligation to sell: a fixed amount; at a fixed time; at a fixed price; of the underlying instrument. TABLE 1: OPTION TERMINOLOGY Call option Put option Exercise price/Strike price In the money Out of the money American Option European Option Premium Traded Option Over the counter option Let us commence with a summary of the terminology surrounding options. This is given in Table 1 and many of the terms should be familiar from the foreign exchange and interest rate exposure sections of the syllabus. USES OF OPTIONS Options have two major uses on financial markets, speculation and hedging. Figure 1 gives an example of how speculators can use options to gamble on share price movements. It will be noted that the payoff from the option investment is far more volatile than from the straight share. This is because with the option, Barney is specualting on the movement in the share price rather than the share price itself. He has effectively geared up his investment. This is a very high-risk strategy and Barney could quite easily lose all of his money. Figure 2 gives a...
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...Definition: In an active portfolio strategy, a manager uses financial and economic indicators along with various other tools to forecast the market and achieve higher gains than a buy-and-hold (passive) portfolio. Tracking error is a measure of how closely a portfolio follows the index to which it is benchmarked. The most common measure is the root-mean-square of the difference between the portfolio and index returns. Many portfolios are managed to a benchmark, normally an index. Some portfolios are expected to replicate, before trading and other costs, the returns of an index exactly (an index fund), while others are expected to 'actively manage' the portfolio by deviating slightly from the index in order to generate active returns or to lower transaction costs. Tracking error (also called active risk) is a measure of the deviation from the benchmark; the aforementioned index fund would have a tracking error close to zero, while an actively managed portfolio would normally have a higher tracking error. Dividing portfolio active return by portfolio tracking error gives the information ratio, which is a risk adjusted performance metric. If tracking error is measured historically, it is called 'realised' or 'ex post' tracking error. If a model is used to predict tracking error, it is called 'ex ante' tracking error. The former is more useful for reporting performance, whereas ex ante is generally used by portfolio managers to control risk. The individual investors who wish...
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... * Futures contracts compared with forward contracts Essential Reading: Hull (2014) Chs. 1 & 2 Additional Reading: Viney, Ch 18, pp. 604 – 613; Ch 19, pp 636-648 Web Resources (Refer to the “External Links” tab on Blackboard) * Financial Pipeline: Derivatives Self-test Quiz Questions Hull Ch. 1: 1.2, 1.4, 1.7 Hull Ch. 2: 2.3, 2.4 (ignore tax questions), 2.5 Tutorial Questions Hull Ch. 1: 1.10, 1.11, 1.12, 1.18, 1.20, 1.21, 1.33 Hull Ch. 2: 2.10, 2.14, 2.16, 2.18, 2.25, 2.26, 2.28 Additional Questions 1. Suppose that on Jan. 4, 2011, an investor bought one March 2011 Share Price Index (SPI) futures contracts at an index level (price) of 4770 (the dollar value of a SPI futures contract is $25 per index point). The investor closed out this futures position on March 17, 2011, at an index level (price) of 5020. What was the investor’s profit (loss) on this transaction? 2. If the initial margin for a SPI futures contract is...
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...pricing objectives? With the introduction of the upgrade, should Clearwater reconsider its pricing strategy? The existing pricing: Number of seats | To end users | Unit cost | Actual unit cost | 10 | 8,000 | 500 | 900 | 20 | 14,000 | 700 | 900 | 30 | 17,250 | 900 | 900 | According to table 1 and 2, because Clearwater is upgrading its products right now, they will design the 30-seat server, so even the customer just want 10-seat or 20-seat, Clearwater will still ship them the 30-seat server with just 10 or 20 seats usable. So in this case, the actual cost of the server will all be 900 dollars. The pricing objectives: For the financial department, the objective is to maximize the profit, so they want the price could be as high as possible; for the sales department, they want the price to be low enough so they can sell more; for the product department, they want the price to be consistent and fair enough as the current product margin model. Now the objectives for each department are different, according to their own interests. So they must have a compromised pricing strategy as soon as possible. Should Clearwater reconsider its pricing strategy? Yes, it is necessary for Clearwater to reconsider its pricing strategy right now. Because they are changing their product strategy, the costs should be change along with the products. If they don’t change the pricing strategy, it will cost the company more when customers buying 10 and 20 seats server. It will cost Clearwater...
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...Gunkel, Swaleh, Quevedo PRELIMINARY STRATEGY REPORT OCTOBER 17, 2012 _______________________________________________________________________________ -(5-10 pages) explaining the various trading strategies you will use :I am just interested to learn about what you plan to try during the next weeks. - The report will be worth 10 points. The grading will be based on the following questions: • Do you understanding how your asset class works? (5 pts) • Did you define clearly and unambiguously your trading strategy? (5 pts) • The key for us is to try to forecast the interest rate for which we need to analyze the impact of monetary policy and QE3, among others. I. Introduction: 1. Asset Selection Eurodollar futures: traded at Chicago Mercantile Exchange (CME Globex Electronic trading platform); convey obligations over a specific notional $ amount in a specific currency $1 million investors use futures to target a cash rate of interest on an underlying benchmark cash product Short term interest rate futures: 3 months Settling price on an exact point in time, when rate of underlying is fixed, the price of cash is agreed upon or fixed every day to create LIBOR settlements (London Interbank offered rate), which is the daily fixing by member banks around London @ 11 am each day. 2. Attributes of Eurodollar Futures: Underlying Instrument | 3-month LIBOR: LIBOR on 3-month U.S.$ deposits | Contract Size | $1,000,000 | Minimum Price Fluctuation | | Contract Months...
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...portfolio strategy ❖ Management of a bond portfolio ➢ PART 3 ❖ Creation of our portfolio ❖ Selection of bonds ▪ Analysis of issuer ▪ Technical analysis ▪ Expectations (including risks) ▪ Investment decision ❖ Investment summary ❖ Performance analysis ❖ Effects of crisis on the bonds chosen ➢ BIBLIOGRAPHY PART 1 What are bonds? In the same way that people borrow money, companies and governments also need to borrow money. A company needs to fund its expansion, conduct market research, develop new products etc., and the problem large corporations encounter is that they need more money than any single bank can provide. This is particularly the case with governments who need to fund everything from infrastructural projects to securing bank loans. Because they can’t borrow large sums from banks they must turn to the public market and raise money by issuing bonds. A bond is a fixed income security or a loan given by the bondholders (individual investors) to the issuer (a company or a government). To incentivize people to invest their own money, an added return over the amount lent must be offered in the form of interest payments, known as coupons. The indenture is the contract between the issuer and the bondholder, setting out all of the obligations of the issuer, e.g. the coupon rate, coupon frequency, maturity date, price, and others...
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...1—Answer Key FIN 413, Spring 2014 Due date: May 22, 2014 Problem 1 The current price of silver is $30.00 per ounce. The storage costs are $0.35 per ounce per quarter payable at the beginning of each quarter. The risk-free rate of interest is 10 percent per annum with continuous compounding for all maturities. Jaime has just entered into a forward contract to buy 10,000 ounces of silver in six-months. a) What is the present value of the storage cost? b) What are the six-month forward price and the value of Jaime’s forward contract? c) Three months later the spot price of silver is 27.50 and the risk-free rate of interest is still 10 percent per annum with continuous compounding for all maturities. What is the value of Jaime’s forward contract? d) Explain why the forward price of silver can be calculated from its spot price and other observable variables whereas the forward price of copper cannot. a) The present value of the storage costs: b) ( ) ( ) The initial value of a forward contract is zero. c) The value of Jaime’s contract is d) Silver is an investment asset. If the forward price is too high, investors will find it profitable to hold more silver and short forward contracts. If the forward price is too low, investors will find it profitable to sell more silver and long forward contracts. Copper is a consumption asset. If forward price is too high, a strategy of buying copper and short forward contracts works. However, because investors generally...
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...fund is looking at 5-year maturity zero-coupon bonds and 4% yield perpetuities to immunize its interest rate risk. How much of its portfolio should it allocate to the zero-coupon bonds to immunize if there are no other assets funding the plan? → 57.14% 42.86% 35.71% 26.00% Duration of the perpetuity = 1.04/0.04 = 26 years Duration of the zero = 1 years 14 = (wz)(5) + (1 – wz)26; wz = 57.14% Learning Objective: 11-04 Formulate fixed-income immunization strategies for various investment horizons. Multiple Choice Difficulty: 3 Hard award: 1.00 point You own a bond that has a duration of 5 years. Interest rates are currently 6%, but you believe the Fed is about to increase interest rates by 29 basis points. Your predicted price change on this bond is ________. (Select the closest answer.) +1.37% → –1.37% –4.72% +4.72% D* = 5/1.06 = 4.72 ∆P/P = –D*(∆y) = –4.72(0.29%) = –1.37% Learning Objective: 11-02 Compute the duration of bonds; and use duration to measure interest rate sensitivity. Multiple Choice Difficulty: 2 Medium 1 of 13 11/29/2014 1:56 PM Assignment Print View http://ezto.mheducation.com/hm_finance.tpx award: 1.00 point You have purchased a guaranteed investment contract (GIC) from an insurance firm that promises to pay you a 7% compound rate of return per year for 5 years. If you pay $10,000 for the GIC today and receive no interest along the way, you will get __________ in 6 years (to the nearest dollar). $13,500 $14,071 ...
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