Finance project on fixed income (Research Paper Sample)

A project on fixed income securities and derivatives. This included currency swaps, option pricing, bootstrapping methodology Answer 1 a) Redemption yield It is the total return anticipated on a bond if the bond is held until the end of its lifetime. Redemption yield is considered a long-term bond yield, but is expressed as an annual rate. In other words, it is the internal rate of return of an investment in a bond if the investor holds the bond until maturity and if all payments are made as scheduled. Par yield A par yield curve is a graph of the yields on hypothetical Treasury securities with prices at par. On the par yield curve, the coupon rate will equal the yield-to-maturity of the security, which is why the Treasury bond will trade at par. Yield to put The annual yield on a bond, assuming the security will be put (sold back to the issuer) on the first permissible dateafter purchase. Bonds are quoted in this manner only if they sell at a price below the put price. Therefore, the yieldincludes interest and price appreciation Yield to worst Yield to worst (YTW) is the lowest yield an investor can expect when investing in a callable bond. (b) Bond equivalent yield = [(par value - purchase price)/purchase price] * [365/days to maturity] = 7.94 % (c) Discount yield = [(par value - purchase price) / par value] * [365/days to maturity] = 7.78% (d) Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest rate, i.e. how the duration of a bond changes as the interest rate changes. Specifically, one assumes that the interest rate is constant across the life of the bond and that changes in interest rates occur evenly. As convexity increases, the systemic risk to which the portfolio is exposed increases. As convexity decreases, the exposure to market interest rates decreases and the bond portfolio can be considered hedged. In general, the higher the coupon rate, the lower the convexity (or market risk) of a bond. This is because market rates would have to increase greatly to surpass the coupon on the bond, meaning there is less risk to the investor. Answer 2 Refer excel for (a), (b) (c) Comparing the yield curves of different types of securities can help investors determine the "relative value" of a bond and can also help to create strategies to increase a portfolio's total return. Investors may wish to compare the German Sovereign yield curve against BB-rated corporate bonds, for example, to see how much additional yield they could capture by assuming some credit risk. One way to do this is to review the "spread," or the difference in yields between different types of securities. Investors can also evaluate spreads from a "current vs. historical" standpoint. In other words, let's say the spread today between a 3 German bonds vs. a 3-year BB corporate bond is +50 basis points. Perhaps the spread was only +35 basis points a year ago. If that's the case, the BB-rated corporate bond, with the +50 basis points yield advantage today, looks particularly attractive. (d) German Bund 10 year yield is 0.13 % (/markets/rates-bonds/government-bonds/germany) whereas the yield for Greece 10 year bond is 8.744 % (http://data.cnbc.com/quotes/GR10Y-GR). The spread is approximately around 8.61 %. This is higher than the long term average of 5.72%.The yield in German Bund is falling. Falling yields mean bond prices are being bid higher as investors look for safe places to park their money. And what's good for bonds is bad for people. Under certain circumstances, such alternative spreads may give a more true and fair view of the development in interest rates over time, e.g. in connection with general macroeconomic analyses. It would be complacent to altogether ignore the possibility that the latest widening of Greek spreads portends another wave of euro zone crisis down the line. Answer 3 * Duration and Convexity can be used to measure the changes in Bond prices in relative to changes in yield rates Duration: It is a measure of the sensitivity of the price (the value of principal) of a fixed-income investment to a change in interest rates. Duration is expressed as a number of years. Rising interest rates mean falling bond prices, while declining interest rates mean rising bond prices. It is calculated as follows Percentage change = percentage change in yield * 100*Duration Convexity - Bond convexity is a measure of the non-linear relationship between price and yield duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates (duration is the first derivative) Change in percentage due to convexity = convexity * ½ * 100 * change in yield squared Estimating a Bond's Price Given Duration, Convexity and Change in Yield.This is done by simply adding the convexity adjustment and the percentage price change due to duration equations to achieve an estimate that is closer than just a duration measure. Total Price change = (-duration x change in yield x 100) + (C*1/2 x change in yield squared x 100) Example: Total Price ChangeUsing the Stone & Co. bonds that had duration of 5.5, let's add a convexity of 93 and an increase of 150 bps in yield. Answer: Price IncreaseTotal Price Change = (-5.5 x .0150 x 100) + (93 x .0150 squared x 100) = -8.25 + 1.046= -7.204so if rates increase by 150 bps, the price will decrease by 7.2% Now let's look at a decrease of 150 bps in yield. Answer: Price Decrease Total Price Change = (-5.5 x -.0150 x 100) + (93 x -.0150 squared x 100) = 8.25 + 1.046= 9.29 So if rates decrease by 150 bps, the price will increase by 9.3 % (b) % change in Price = - Modified Duration * Change in yield *100 + Convexity *1/2 * Change in yield squared * 100 $ amount change of increase in yield -25.0369 $ amount change for decrease in yield 36.55185 (c) Interest rate sensitivity is a measure of how much the price of a fixed-income asset will fluctuate as a result of changes in the interest rate environment. Securities that are more sensitive will have greater price fluctuations than those with less sensitivity. One of the primary objectives of asset/liability management is to maximize the net interest margin while minimizing the earnings risk associated with changes in interest rates. When a bank's assets and liabilities do not reprice at the same time, the result is a change in net interest income. The change in the value of assets and the change in the value of liabilities will also differ, causing a change in the value of stockholder's equity. The various risks associated with managing interest rate Reinvestment risk--variability in realized yield caused by changing market rates for coupon reinvestment. Price risk--variability in realized return caused by capital gains/losses or that the price realized may differ from par. Price risk and reinvestment risk offset one another, depending upon maturity and coupon rates. (d) The duration of fixed income liabilities is 1.5 years whereas the duration of loan deposits is 3 years. This has created a duration gap in the bank Duration gap- It is a financial and accounting term and is typically used by banks, pension funds, or other financial institutions to measure their risk due to changes in the interest rate. This is one of the mismatches that can occur and are known as asset liability mismatches. Another way to define Duration Gap is: it is the difference in the price sensitivity of interest-yielding assets and the price sensitivity of liabilities (of the organization) to a change in market interest rates (yields) Duration gap = duration of earning assets – duration of paying liabilities *(paying liabilities/ earning assets) = 3-1*(99/100) = 2 * .99 =1.98 So this means that asset duration is more than the duration of liabilities. The change is asset values happen more quickly than change is liabilities Positive DGAP indicates that assets are more price sensitive than liabilities, on average. Thus, when interest rates rise (fall), assets will fall proportionately more (less) in value than liabilities and EVE will fall (rise) accordingly To immune the bank from rate changes, it needs to decrease the asset duration by 1.98 years. Or it can increase the liability duration by 1.98 * 99/100 = 1.96 years Various strategies that can be used are as follows Zero-coupon bonds have no reinvestment risk. The duration of a zero equals its maturity. Buy a zero with the desired holding period and lock in the yield to maturity. To assure that the promised yield to maturity is realized, investors select bonds with durations matching their desired holding periods. (Duration-matching approach). Selecting a bond maturity equal to the desired holding period (maturity-matching approach) eliminates the price risk, but not the reinvestment risk. Yield curve strategy - When the U.S. economy hits its peak, the yield curve typically inverts, with short-term rates exceeding long-term rates. As the economy contracts, the Federal Reserve typically increases the money supply, which causes the rates to fall and the yield curve to return to its "normal" shape. To take advantage of this trend, when the yield curve inverts, banks could a)Buy long-term non-callable securities b )Prices will rise as rates fall c ) Make fixed-rate non-callable loan...