Bond portfolio

We perform an analysis in which we compare bonds with similar characteristics within the same industry. This is a common analysis undertaken by bond portfolio managers looking to invest in a particular industry. 

Fisher, L., Leibowitz, M., 1983. Effects of alternative anticipations of yield curve behaviour on the composition of immunized portfolios and on their target returns. In Kaufmann, G. et al. (Ed.), Innovations in Bond Portfolio Management. Jai Press. 

An investor s corporate bond portfolio has an identical duration to a benchmark portfolio of government bonds, and an OAS of 50 basis points. Assume that the portfolio has a spread duration of 5. During a 12-month holding period, the excess income of the portfolio compared to government bonds is 0.25%. How much can the OAS widen before the corporate bond portfolio begins to underperform the government portfolio ... 

As one might expect the yields on bonds are correlated, in most cases very closely positively correlated. This enables us to analyse interest-rate risk in a portfolio for example, but also to model the term structure in a systematic way. Much of the traditional approach to bond portfolio management assumed a parallel shift in the yield curve, so that if the 5-year bond yield moved upwards by 10 basis points, then the 30-year bond yield would also move up by 10 basis points. This underpins traditional duration and modified duration analysis, and the concept of immunisation. To analyse bonds in this way, we assume therefore that bond yield volatilities are identical and correlations are perfectly positive. Although both types of analysis are still common, it is clear that bond yields do not move in this fashion, and so we must enhance our approach in order to perform more accurate analysis. 

A fundamental property is that an upward change in a bond s price results in a downward move in the yield and vice versa. This result makes sense because the bond s price is the present value of the expected future cash flows. As the required yield decreases, the present value of the bond s cash flows will increase. The price/yield relationship for an option-free bond is depicted in Exhibit 1.9. This inverse relationship embodies the major risk faced by investors in fixed-income securities—interest rate risk. Interest rate risk is the possibility that the value of a bond or bond portfolio will decline due to an adverse movement in interest rates. 

There are two main types of credit risk that a bond portfolio or position is exposed to. They are credit default risk and credit spread risk. Credit default risk is defined as the risk that the issuer will be unable to make timely payments of interest and principal. Typically, investors rely on the ratings agencies—Fitch Ratings, Moody s Investors Service, Inc., and Standard 8c Poor s Corporation—who publish their opinions in the form of ratings. 

We will discuss two approaches for assessing the interest rate risk exposure of a bond or a portfolio. The first approach is the full valuation approach that involves selecting possible interest rate scenarios for how interest rates and yield spreads may change and revaluing the bond position. The second approach entails the computation of measures that approximate how a bond s price or the portfolio s value will change when interest rates change. The most commonly used measures are duration and convexity. We will discuss duration/convexity measures for bonds and bond portfolios. Finally, we discuss measures of yield curve risk. 

DIHBir 4.5 Illustration of Full Valuation Approach to Assess the Interest Rate Risk of a Bond Portfolio for Four Scenarios Assuming a Parallel Shift in the Yield Curve, 2-Bond Portfolio (hoth bonds option-free)... 

To illustrate the calculation, consider the following three-bond portfolio in which all three bonds are Irish government securities. Exhibit 4.25 presents a brief description for each bond that includes the following full price per 100 of par value, its yield, the par amount owned, the market value and its duration assuming a settlement date of 6 June 2003. Since these securities are priced with a settlement date between coupon payments dates, the market prices reported are full prices. The... 

EXHIBIT 4.25 Summary of a Three-Irish-Govemment-Bond Portfolio... 

For example, consider the 3-bond portfolio given in Exhibit 4.25. Suppose that we calculate the dollar change in market value for each bond in the portfolio based on its respective duration for a 50 basis point change in yield. We would then have ... 

Thus, a 50 basis point change in all rates will change the market value of the 3-bond portfolio by 292,231.33. Since the market value of... 

The most popular version of this approach was developed by Thomas Ho in 1992. This approach examines how changes in US Treasury yields at different points on the spot curve affect the value of a bond portfolio. Ho s methodology has three basic steps. The first step is to select several key maturities or key rates of the spot rate curve. Ho s approach focuses on 11 key maturities on the spot rate curve. These rate durations are called key rate durations. The specific maturities on the spot rate curve for which a key rate duration is measured are 3 months, 1 year, 2 years, 3 years, 5 years, 7 years, 10 years, 15 years, 20 years, 25 years, and 30 years. However, in order to illustrate Ho s methodology, we will select only three key rates 1 year, 10 years, and 30 years. 

Key rate durations are most useful when comparing two (or more) bond portfolios that have approximately the same duration. If the spot curve is flat and experiences a parallel shift, these two bond portfolios can be expected to experience approximately the same percentage change in value. However, the performance of the two portfolios will generally not be the same for a nonparallel shift in the spot curve. The key rate duration profile of each portfolio will give the portfolio manager some clues about the relative performance of the two portfolios when the yield curve changes shape and slope. 

Large coupon payments are another key factor to watch to assess each country s relative performance, as the investor s domestic bias could favour that part of these payments would come back to the same market. Additionally, by reinvesting these flows (coupons and redemptions) in the same market they come from, the country and credit composition of the bond portfolio would not be altered. 

Consider the opposite scenario, bond yields are expected to fall substantially and in the near future. In this case, the fund manager will be seeking to extend the maturity or duration of the bond portfolio. However, instead of adopting a physical bond-switching strategy government bond futures will be used. Here is such a scenario ... 

Analysts are now advising that the slump in equity prices has bottomed out, but that further reductions in the rate of interest are a possibility. The fund manager decides to leave the composition of the bond portfolio unchanged, but in view of the likely rise in share prices, decides to realign the portfolio weightings so that a 50/50 bond/equity mix is achieved. 

The bond portfolio has the following characteristics Modified duration is 7.4908 yield is 4.595%, current valuation is 300,000,000. The BPV of the Euro-Bund future is 72.03. 

The question is how many bond futures need to be shorted to achieve the desired 25% reduction in weighting From the previous example, the BPV of the bond portfolio can be found by equation (16.15). In this case the BPV of the desired reduction will be given by... 

The above examples have focused on the use of the Euro-Bund future as a vehicle for achieving a particular bond portfolio exposure. As indicated earlier, there are several other futures contracts available in the European arena and these could be used in the same way as described above. The futures contracts could also be used to alter the maturity characteristics of the portfolio by using, for example, futures contracts constructed around shorter or longer dated instruments than those currently held in the portfolio. The fact that the contracts can be bought or sold on margin, that the major contracts are liquid and span the European markets, and their flexibility of use make them essential financial market instruments. 

At the time, the June 2003 Euro-BUND future is trading at 116.42, and the cheapest-to-deliver (CTD) bond for the June 2003 futures contract is the 5% bond maturing on 4 January 2012, and having a conversion factor of 0.9341. The PVBP (or DVOl) for the CTD bond is 0.0788, while that for the bond actually held is 0.0840. The hedge ratio for the bond portfolio is therefore... 

Unhedged, the bond portfolio will lose 500,000 for every 1% fall in the bond price. The ATM put hedges this loss, while allowing the bond portfolio to profit if bond prices rise. However, the up-front cost of 627,480 may seem onerous. 

An alternative is to hedge with cheaper OTM puts, for example, the 115 puts priced at only 0.64, costing 318,720—half the price of the ATM options. As the revised payoff diagram of Exhibit 17.21 shows, however, while the investor benefits more when bond prices rise (because the premium wasted is smaller), the maximum loss is greater when bond prices fall. This is because the bond portfolio remains unhedged while bond prices fall 1.42%, until the put strike is reached, losing around 700,000. Together with the premium of around 300,000, the investor could lose more than 1 million, as the chart shows. 

Convexity comes into play when yield curve changes are moderate to large and serves to increase the value of the bond irrespective of whether the yield rises or falls. In other words, if yields rise, then bonds with positive convexity fall less than expected from duration alone, and when yields fall, bond prices rise more than expected. To put it bluntly, convexity is good for a bond portfolio, but it is exceptionally hard to actively manage a credit portfolio and maximise convexity at the same time. 

Exhibit 26.7 is an illustration of a bulleted exposure relative to the benchmark crafted on a duration-neutral basis. Exhibit 26.8 illustrates the effect of a curve steepening on a two-bond portfolio (barbell) to a one-bond portfolio (bullet) with identical dollar durations. As can be observed from the exhibit, the 2-30 part of the curve has steepened by 100 bp, with the two year yields falling 50 bp, 10 year yields rising 50 bp, and the 5-year yields unchanged. In the example, such a scenario would cause the barbell portfolio to underperform the bulleted one by 1.07%... 

A QUANTITATIVE APPROACH TO DETERMINE OPTIMAL BOND PORTFOLIOS ... 

A straightforward interpretation of the parameters rmin = -5% and p = 10% is that an investor with a moderate risk tolerance and a 10-year horizon, for example, would allow his bond portfolio on average to fall short of 5% in one of 10 years. 

The database consists of 275 monthly data sets. For a 5-year investment horizon, 60 data sets are required for every rolling computation of the optimal portfolio. This means that 215 (= 275 - 60) rolling calculations must be run for the 5-year investment horizon (3 year 239, 10 year 155). Averaging the weights over all 215 (239, 155) rolling calculations gives an indication of the optimal allocation of funds in a bond portfolio for a 5-year horizon (3-year, 10-year horizon). 

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