Interest Rate Risk and Currency Risk Management

The validity of the yield to maturity as a measure of relative value in bonds and explain an alternative yield measure which is conceptually superior. Yield to maturity (YTM) is the annualised rate of return in percentage terms of a fixed income instrument (e. g. ) bond, taking into account coupon rates, frequency of payouts, and capital gains or losses. YTM is fundamentally the interest rate that will make the present value of the cash flows equal to the price. The calculation takes into account the current market price, par value, coupon interest rate and time to maturity.
Yields are shown on a before- and after-tax basis. In order to discuss the validity of YTM as a measure of relative value in bonds, one needs to critically evaluate the measure in terms of strengths and weaknesses. When purchasing bonds, at market price, there are three numbers commonly used to measure the annual rate of return on investment. Firstly, the coupon rate, which shows the annual payout as a percentage of the bond’s par value. Secondly, the current yield, illustrating the annual payout as a percentage of the current market price one actually pays.
Lastly, YTM which illustrates the composite rate of return of all payouts, coupon and capital gain (or loss). The capital gain or loss is the difference between par value and the price you actually price. Out of the three other measures, YTM provides the best measure for the return rate, as it includes all aspects of investment. In order to calculate YMT, certain conditions need to be satisfied just like other composite payouts. Irregardless of interest rates, merely calculate the present values of all payouts and then add up these present values to ascertain a value (equalling the initial investment).

The left side of the equation represents the different compound interest curves, all starting out now, and each one ending at the moment that the payout it corresponds to takes place. Most of these curves will lie pretty low to the axis, as they only grow to a value of the coupon payment. The very last curve will be a lot taller, and end up at the par value B. The advantage with YTM is the problems of matching form, so people have managed to create programmable calculators and computer programs to aid the computation of r.
Alternatively, differential calculus can also be employed to calculate r by trial and error. When r is attained and reapplied back into the equation, it will become evident that the YTM calculated is greater than the current yield, in turn is greater than the coupon rate. Several underlying assumptions exist behind the calculations. These assumptions are critically analysed below. Investors using this measure will only realise the yield at the time of purchase providing the bonds are held to maturity and coupon payments can be reinvested at the computed yield to maturity.
Therefore, the two underlying conditions are that bonds will be held to maturity and the coupon payments are reinvested at the identical rate. Another major assumption is the reinvestment rate is the yield to maturity. A major drawback to YTM as a measurement tool is it relies on investors holding their bond positions till maturity. If however, the investor decides (for whatever reason) to sell his position, this method of measuring yield is completely ineffective (unlike realised compound yield discussed in more detail later on).
In the real world, constant changes are taking place; therefore, assumption investors hold bonds till maturity may not have such high standings. Given the predominance of the assumption the reinvestment rate is the yield. A major validity issue to proclaim is reinvestment risk. Reinvestment risk is fundamentally when investors’ reinvestment rates are not equal to the YTM rates. Are two primary attributes to reinvestment risk taking into account we are discussing bonds solely. First attribute arises from the issue of maturity. A longer maturity period leads to a larger reinvestment risk.
Reason for a larger risk stems from the fact it is difficult to reinvest the interest payments at exactly the YTM rate, over a longer maturity period time means more payments have to be made. If each payment is not exactly equal, at date of maturity a significant difference will have been formed. Second attribute arises from the issue of the size of coupon payment. Providing maturity and YTM remains constant, a higher coupon rate will mean the more dependent the bond’s total return will be on the reinvestment in order to produce the yield to maturity anticipated at time of purchase.
Size of coupon payment has various effects on different bonds. For example, when maturity and yield to maturity are constant, premium bonds are subject to greater dependency on the interest-on-interest coupons than bonds selling at par. In addition, discount bonds are even less dependent on the interest-on-interest components than bonds selling at par. While discussing the various bonds, it is worth noting that zero-coupon bonds have zero reinvestment risk because yield earned on this type of bond held to maturity is equal to the promise yield to maturity (ignoring the annual income tax bite).
In the real world, it is virtually impossible to reinvest the interest payments at exactly the YTM rate. As the YTM rate is usually accumulated at a lower interest rate before being reinvested. Hence, YTM always overstates the true return. Leading to interest earnings spent instead of reinvested. When interest earnings are spent instead of being reinvested, the return will be lower. It is important to recognise that the interest payments are normally trimmed by a tax bite, making it even more impossible to reinvest the full amount of each payment.
Another fault with YTM as a measure of relative value in bonds is due to the fact that bonds interest payments are usually made twice a year at half coupon rate. Therefore, compounding of the reinvested interest payments come up with higher annualised returns than once a year reinvested payments at the full coupon rate. This fault is why YTM is usually specified in terms of bond-equivalent yield. Deducing YTM slightly plays down the YTM when viewed as the annualised compound rate of return. Once more bring us back to the issue of reinvestment risk.
In conclusion, based upon the arguments put forth, it is fair to say YTM is a measure that only approximates the true return and is not completely accurate. Nevertheless, is a useful measure since it is a quick way to make sketchy comparisons of returns on bonds of different coupons and maturities. Providing assumptions hold true, taxes did not exist, yield curves were flat and interest rates remained constant over the life of the bond, YTM would be a more accurate measure of return. YTM becomes a less accurate measure when yield curve steepens and/or when purchase price deviates further from par value.

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