5measurerisk

5measurerisk - ACTSC 445 Asset-Liability Management...

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Unformatted text preview: ACTSC 445: Asset-Liability Management Department of Statistics and Actuarial Science, University of Waterloo Unit 5 – Measuring Interest-Rate Risk References (recommended readings): Chap. 9 of Fabozzi et al. As mentioned before, the holder of a fixed income security or portfolio is exposed to interest-rate risk. That is, if interest rates increase, the price of the security will drop, which may result into a loss for the investor if he/she needs to sell the security before maturity. It is important for investors to assess the sensitivity of fixed income securities to changes in interest rates in a precise, quantitative way, so that the interest-rate risk can be better understood. In this unit, we’ll see different ways to do that: 1. The full-valuation approach; 2. Price value of a basis point; 3. Duration and convexity: we’ll spend most of our time on that approach. We will also discuss alternative definitions of duration that can be used in more complex settings. Before we go over these different approaches, it is important to mention that in what follows, most of the time we will look at interest rates changes as being observed on ytm’s. Also, unless otherwise stated, we assume bonds pay semi-annual coupons. As an example, we show in Table 1 how the price of different bonds vary when the ytm goes from 4% to different values ranging between 2 and 6%. All rates below are assumed to be annual, compounded semi-annually. Figure 1 gives a graphical depiction of the numbers given in Table 1. Table 1: Bond prices as a function of yield ytm 4%-4 year 4%-12 year 8%-4 year 8%-12 year 2% 107.65 121.24 122.96 163.73 3% 103.74 110.02 118.71 150.08 3.5% 101.85 104.87 116.66 143.79 3.9% 100.37 100.95 115.05 138.99 3.99% 100.04 100.09 114.69 137.94 4% 100 100 114.65 137.83 4.01% 99.96 99.91 114.61 137.71 4.1% 99.63 99.06 114.25 136.67 4.5% 98.19 95.40 112.68 132.18 5% 96.41 91.06 110.76 126.83 6% 92.98 83.06 107.02 116.94 Equivalently, we can compute the instantaneous percentage change of the bond’s price for the different changes in the ytm: 1 Figure 1: Bond prices as a function of yield Table 2: Bond’s price percentage change as a function of yield ytm 4%-4 year 4%-12 year 8%-4 year 8%-12 year 2% 7.65 21.24 7.24 18.79 3% 3.74 10.02 3.54 8.89 3.5% 1.85 4.87 1.75 4.32 3.9% 0.37 0.95 0.35 0.85 3.99% 0.04 0.09 0.03 0.08 4.01%-0.04-0.09-0.03-0.08 4.1%-0.37-0.94-0.35-0.84 4.5%-1.81-4.60-1.72-4.10 5%-3.59-8.94-3.40-7.98 6%-7.02-16.94-6.66-15.16 Several comments about the sensitivity of the bond’s price to changes in interest rates can be observed from Tables 1 and 2: • For small changes in the ytm, the percentage price change for a given bond is roughly the same, whether the ytm goes up or down....
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This note was uploaded on 09/10/2010 for the course ACTSC 445 taught by Professor Christianelemieux during the Spring '09 term at Waterloo.

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5measurerisk - ACTSC 445 Asset-Liability Management...

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