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Imarticus Learning www.imarticus.org PGGFP: Case Studies

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Single Period Immunization Case Study #2 on Bond Strategies

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The Challenge Context Advice The Process Results Key Takeaways THE AGENDA Bond Strategies Single Period Immunization

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CONTEXT Sagarika Ghosh is a fixed income analyst working at A- One Securities in Mumbai. A-One Securities is a leading fixed income broker-dealer in the Indian market. Sagarika has been given a problem by her boss, Ravi Gupta, and has been asked to analyze and give her opinions. A broker-dealer is a natural person, a company or other organization that engages in the business of trading securities for its own account or on behalf of its customers. Broker-dealers are at the heart of the securities and derivatives trading process. DID YOU KNOW ?

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The company plans to invest in suitable bonds so that it can be assured of meeting its commitment. AIF Ltd. is an American insurance company. that has employed A-One Securities as its broker. AIF Ltd. needs to pay an assured return of 8.40% on a policy after 8 years. The principal amount is 5,000,000 INR. The company has approached A-One securities, its broker, to suggest a suitable investment product. AIF wants to protect itself against the specter of a one- time change in interest rates right at the outset. THE CONTEXT

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AIF Ltd. is an American insurance company. It needs to pay an assured return of 8.40% on a policy after 8 years. The principal amount is 5,000,000 INR. The company plans to invest in suitable bonds so that it can be assured of meeting its commitment. AIF wants to protect itself against the specter of a one-time change in interest rates right at the outset. The company has approached A-One securities, its broker, to suggest a suitable investment product. Alternate to previous screen

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DATA Sagarika has a choice of three debt instruments. Choice of Debt Instruments BOND A BOND C BOND B As of 2009, the size of the worldwide bond market (total debt outstanding) is an estimated $82.2 trillion. DID YOU KNOW ?

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DATA Take a close look at the features of each instrument. Face Value: Rs.. 1,000/- Years to Maturity: 12 Coupon Rate: 12% pa. YTM: 8.40% Bond A Face Value: Rs.. 1,000/- Years to Maturity: 12 Coupon Rate: 8.40% pa. YTM: 8.40% Bond B Face Value: Rs.. 1,000/- Years to Maturity: 10 Coupon Rate: 12% pa. YTM: 8.40% Bond C All three bonds are scheduled to pay coupons on an annual basis. The coupon is the interest rate that the issuer of the bond pays to the holder. Usually this rate is fixed throughout the life of the bond. DID YOU KNOW ?

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THE CHALLENGE What are the prices of the three bonds? How many bonds are required to implement the immunization strategy? What are the durations of the three bonds? Which of these bonds is suitable for an immunization strategy? A B CD Sagarika needs to find solutions to the following questions. While most bonds pay interest on a semi-annual basis, some may even pay interest on a monthly, quarterly or annual basis. DID YOU KNOW ?

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Having identified a suitable bond, Sagarika will have to compute and demonstrate that: At the end of 8 years The cash flow will be adequate to meet the liability irrespective of a given one-time change in interest rates THE CHALLENGE Bonds typically trade in $1000 increments and are priced as a percentage of par value (100%). DID YOU KNOW ?

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5 increments and decrements of 20 basis points on either side of the prevailing interest rate of 8.40 % per annum ! She needs to show that the bond which is selected by her will be adequate to meet the liability of the insurance company. Sagarika is contemplating considering: THE CHALLENGE Nearly all of the $822 billion average daily trading volume in the U.S. bond market takes place between broker-dealers and large institutions in a decentralized, OTC market. DID YOU KNOW ?

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THE CHALLENGE Text NOW CONSIDER THINGS FROM ANOTHER PERSPECTIVE.. Will Sagarika’s immunization strategy work? The interest rate increases by 20 basis points from its current level of 8.40% at the outset. The interest rate once again increases by another 20 basis points after two years. Assumptions: Immunization strategy adjusts the portfolio duration to match the investor's investment time horizon, thereby ensuring a bond is "immune" to fluctuating interest rates. DID YOU KNOW ?

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ADVICE Sagarika’s boss, Ravi, advises her to make use of the following functions in EXCEL. Present Value (PV) PV or Present Value for computing the price of a bond on a coupon date. The required parameters are: Rate discount rate nper # of periods (coupons) pmt periodic payment (coupon) fv future value (Face value in the case of a bond) Future Value (FV) Note: In EXCEL cash flows in opposite directions have the opposite sign. That is if the inflows are positive then the investment is negative and vice versa. FV or Future Value for computing the future value of a stream of cash flows. The required parameters are: Rate Reinvestment rate nper # of periods pmt periodic payment PV Present Value (if and only if there is an initial investment at the very outset)

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ADVICE DATA THE PROCESS Reference Document Click here Sagarika systematically went about resolving the questions posed to her….

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THE PROCESS: FORMULAS f x Duration of a Bond Where: CF t = The cash ﬂow at time ‘t’ The cash ﬂows from the ﬁrst to the penultimate period will be equal to C/2 for a bond paying coupons on a semi-annual basis. The terminal cash ﬂow will be equal to the semi-annual coupon plus the face value. In mathematical terms: P= The dirty price of the bond The answer to the above equation will be in terms of the coupon periods. So it has to be divided by the coupon frequency in order to annualize it. Thus, if the bond were to pay semi-annual coupons, the answer will be in half- years and will have to be divided by two.

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THE PROCESS: FORMULAS f x Where: y =the periodic yield to maturity c = the periodic coupon rate N = the number of coupons There is a concise formula for the duration: Thus, if the bonds were to pay coupons semi-annually: c will be the half yearly coupon rate y will be the semi-annual yield to maturity Duration of a Bond

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THE PROCESS: FORMULAS f x Consider a bond with a maturity of T years and a face value of M. Let the annual coupon be C and the prevailing interest rate be r. If the interest rate does not change subsequently all the coupons will be reinvested at r% per annum. Assume that the bond is sold after N years. At that time it will have T-N years to maturity. The YTM at the time of sale is r% by assumption. The future value of all the coupons at the end of N years will be: The terminal price of the bond will be: The cash ﬂow from both the sources after N years will be the sum of the two.

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1.Project all the cash flows from each bond. 2.Discount each cash flow at the yield to maturity to arrive at the present values. 3.The dirty price is the sum of all the present values. A What are the prices of the three bonds? ADVICE DATA THE PROCESS Sagarika systematically went about resolving the questions posed to her. BONDDIRTY PRICE Bond A1118.1177 Bond B1000.0000 Bond C1237.2646 Question ProcessAnswer 1.Divide each of the present values by the dirty price to arrive at the weights. 2.Each of the weights should be multiplied by the corresponding time period. 3.The column of products must be summed up to arrive at the duration. B What are the durations of the three bonds? BONDDURATION Bond A7.7438 years Bond B8.0025 years Bond C6.7028 years

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ADVICE DATA THE PROCESS Sagarika systematically went about resolving the questions posed to her. To immunize the portfolio we need to invest in an asset whose duration is equal to the investment horizon. Since the investment horizon is given as 8 years, the appropriate asset is Bond B. Bond B The present value (PV) of the investment should be equal to the PV of the liability. The PV of the liability is Rs.. 5,000,000 and the dirty price of Bond B is Rs.. 1,000. Hence, we need to acquire 5,000 bonds. 5,000 Bonds Question Process Answer C D Which of these bonds is suitable for an immunization strategy? How many bonds are required to implement the immunization strategy?

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ADVICE DATA THE PROCESS Sagarika systematically went about resolving the questions posed to her. E Let us assume the interest rate jumps to 8.60% from 8.40%. We need to find the future value of 8 investments of Rs. 84 per year after 8 years, assuming a reinvestment rate of 8.60%. The answer is Rs. 913.07. We need to price the bond after 8 years assuming a YTM equal to the new interest rate of 8.60%. Since Bond B is a 12 year bond, it will have a maturity of 4 years after 8 years. The price is Rs. 993.46. The total terminal cash flow when the investment is liquidated after 8 years is Rs. 1906.53. This is per bond. So the proceeds from 5,000 bonds is Rs. 9,532,674. The amount to be repaid is the future value of Rs. 5,000,000 with 8.40% interest per annum. This amounts to Rs. 9,532,444. Thus there is a surplus of Rs. 230. It can be shown that there is a surplus for the situation corresponding to each of the assumed interest rate changes. Hence the portfolio is protected against a one-time shift in interest rates right at the outset. Process How will Sagarika demonstrate that the cash flows at the end of 8 years will be adequate to meet the liability?

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ADVICE DATA THE PROCESS Sagarika systematically went about resolving the questions posed to her. F In this case, the interest rate jumps from 8.4% to 8.6% at the outset, and then to 8.8% after two years. The future cash inflow from a bond may be calculated as follows. There will be an inflow of Rs. 84 after one year. It will be invested at 8.6% for one year and at 8.8% for the remaining 6 years. This amounts to Rs. 151.32. The remaining coupons can be reinvested at 8.8%. There are 7 more remaining coupons. Their future value at the end of the 8th year is 768.11. The sale price of the 4 year bond if the YTM is 8.8% = Rs. 986.98. The terminal cash inflow per bond is Rs. 1906.41. The total inflow from 5000 bonds is Rs. 9,532,055. Thus there is a deficit of Rs. 389. Hence if interest rates were to change at the outset and then again subsequently, our immunization strategy need not work. Process If interest rates were to change at the outset and then again subsequently, would the immunization strategy work?

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Sagarika documents the results to the questions posed to her, which she summarizes as shown below. QuestionSolution A) What are the prices of the three bonds?Bond A – Rs. 1118.1177 Bond B – Rs. 1000.0000 Bond C – Rs.. 1237.2646 B) What are the durations of the three bonds?Bond A – 7.7438 years Bond B – 8.0025 years Bond C – 6.7028 years C) Which of these bonds is suitable for an immunization strategy? Bond B D) How many bonds are required to implement the immunization strategy? 5,000 bonds THE RESULTS

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QuestionSolution E) Demonstrate that the cash flows at the end of 8 years will be adequate to meet the liability. There is a surplus for the situation corresponding to each of the assumed interest rate changes. Hence the portfolio is protected against a one-time shift in interest rates right at the outset. F) If interest rates were to change at the outset and then again subsequently, would the immunization strategy work? The immunization strategy need not work. THE RESULTS

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Proceeds at which the bond is liquidated Return from reinvested coupons Market or Price Risk Reinvestment Risk DATA KEY TAKEAWAYS So, what did Sagarika learn from this experience? Types of Risks: Holders of bonds are exposed to two kinds of risks. Price risk is the risk that interest rates may rise after a bond is acquired. All bonds are not held till maturity. Reinvestment risk is the risk that interest rates may decline after a bond is acquired. If so, all the coupons that are received during the period that the investor holds the bond, will have to be reinvested at lower rates of interest. Market or Price Risk: Bond held to maturity? The investor will get back the face value. Yes Investor will have to sell it at the prevailing market price. No Reinvestment Risk The two risks work in opposite direction. Risk TypeRatesInvestor Sentiment Reinvestment Price / Market If a portfolio is immunized: Immunization: Immunization is a strategy for ensuring that the investor is protected against interest rate risk.

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DATA KEY TAKEAWAYS So, what did Sagarika learn from this experience? There are two conditions that need to be satisfied if a bond is to be immunized against a one-time change in interest rates right at the outset. The value of the investment in the bond must be equal to the present value of the liability. The duration (not the time to maturity) of the bond must be equal to the investment horizon. If these two conditions are satisfied: No matter what the change in rates happens to be, the bond investment will yield a surplus over the anticipated liability. Cash inflows may be more, but cannot be less. ! This argument will hold true only if there is a one-time interest rate change right at the outset. If there were to be a second rate change subsequently, then we are not assured that the proceeds from our investment will be adequate to meet our liability. 1 2

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Q A & Thank You For Your Attention

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