Financial Management and Bond Valuation - Coursework Example

FINANCIAL MANAGEMENT By Bond Valuation A bond is a debt instrument in which investors’ loans out money to either a governmental or a corporate entity that has borrowed the money for a defined period of time and a pre-determined interest rate. The issuer of the bond usually states the maturity date, which the date that the bond will mature. The coupon payments which are the interest payments that will be remitted to the bond-holder after a specific period of time for example six months and the face value of the bond refers to the amount of money that the bond holder will be paid at maturity (Asquith et al., 2010, pp.236-39) Bonds are valued using the time value of money principle where due to its earning capacity, money available at present are more worthy than the same amount in the future. The interest rates are treated like an equal annual cash flows streams while the face value is treated as a lump sum (Minton, 1997, pp.28). Questions a. Calculations are in excel b. Modified duration is the percentage change in bond value for every 100 points change in yield as long as long as the expected cash flows do not change with the change in yield.  Where k is the number of periods, n is the number of periods to maturity, Yield is the yield to maturity of the Bond and PVCF is the present value of the discounted cash flows at the yield to maturity. The calculations are show in the excel file attached. Question 2 Standard and Poor 500 (S&P 500) is a capitalization-weight index of the best performing five hundred publicly listed stock in the United States. This covers about 75% of the American equity market by capitalization. The data included in the index includes the financials such as the stock price, the market capitalization earnings and so on (Anderson, 1997, pp.456). The intrinsic value of stock is derived from estimating and discounting the future cash flows from the stock and it simply implies the estimated value of stock today. Investor and analysts to state the relationship between the stock price and the intrinsic value have used it. If the intrinsic value is greater than the current stock price, the asset should be purchase or keep hold of it if it is already owned. The asset is correctly valued if the current stock price is equal to the intrinsic value. Nevertheless, if the intrinsic value is less than the current stock price, the asset is overvalued and therefore should be avoided at all cost and if it is already held, it should be sold. Divided discounted model of stock valuation is uses a discounted cash flow model. It states that the value of stock is equal to the current value of all the future payments to which the stock holder is entitled. In this case the payments are in form of dividends. Where P0 is the present value of the stock, Dt is the expected dividend per share and r is the required rate of return per share. Calculations of the intrinsic value were carried out in excel and the results are as in the table below. Stock Name. Current Value Intrinsic Value SYSCO 40.26 33.55 Cintas 73.15 86.06 The greatest assumption by the dividend discounted model is that the dividends are steady or will continue to increase at a constant rate for the foreseeable future. This is absurd because even for the blue chip stock, it is difficult to forecast the discount that will be paid out in one or two years’ time because the dynamic business may change in the course of the period. The model can be used for firms that operate in stable businesses or in highly regulated sectors as that will limit the expansion of the firm into new businesses. Question 3 Efficient Frontiers Portfolio variance is a measure of the fluctuations of the actual returns of the securities or assets that makes up the portfolio. A minimum variance portfolio therefore is an optimal combination of risky assets which when combined results in the lowest possible risk level for the expected rate of return. Each investment in such a portfolio is hedged with an offsetting investment thus lowering the risk levels. The offsetting investment depends on the level of risk that is involved as well as the level of return that the investor is willing to accept. Individual investments in a minimum variance portfolio as are generally more risky than the whole portfolio combined ( Broadie, 1993, pp.21-58). On the other hand, an efficient portfolio is the one that offers the highest expected return of a given revel of risk as measured by variance of even the standard deviation of return. Thus there is no portfolio with a better level of expected return or a lower volatility level that can be constructed with securities available in the market than an efficient one. Short selling is disposing of an asset not owned by the seller or has been borrowed. The motivation behind short selling is that the price of the asset will decline and therefore the seller to buy it back, but now at a profit. Sometimes short selling may be driven by speculative reasons or a desire to downsize a risky position in the same security or a related one. Although speculation has been negatively perceived, it is a well calculated moves that involves assessment of the market and taking risks where the odds appears to be in your favour. If the wrong strategies are applied, speculators can assume a high loss but can as well make very high returns when market forces moves in their favour. Another reason for short selling is hedging in order to protect other long positions with offsetting short positions. Derivation of the minimum variance The main assumptions in Markowitz portfolio model is that investor’s base their preference of risky assets on both the expected return, and the standard deviation, as a measure of the degree of risk involved. Therefore, the portfolio selection headache to the investor can be expressed as a return maximization in relation to the risk of the investment. This problem can be expressed in a quadratic form mathematically. For example with assets A and B whose portfolio consists of a return of, the portfolio should be chosen in such a way that the risk is minimized. That is, The minimum variance portfolio weights of the two assets are depicted in Table 1 below. The correlation of two assets Weight of Asset A Weight of Asset B ρ= 1 ρ= -1 ρ= 0 Table 1: The minimum variance portfolio of assets A and B without short selling. From the above information, we can generalize that for a portfolio containing N risky assets, the minimum portfolio weights can be obtained by minimizing the following function. The approach can be used to calculate the minimum variance for any level of expected return. The numerous calculations involved are tiresome and therefore it is advisable to use a computer to carry them out. Using a computer also increases the accuracy by minimizing the errors. Plotting the possible asset combination in a risk-space diagram define the possible portfolio region in the graph as shown in Figure 1. The efficient frontier is the line along the upper border and is a representative of the portfolios with the lowest risk at any given level of return. In mathematical terms, the intersection of the set of portfolios with a minimum variance and the set with the maximum returns is what is referred to as the efficient frontier. Figure 1: A risk-return space diagram depicting investment opportunities for a set of assets A and B. Portfolio set that lies along the curve VA would not be appealing to an investor because they are not maximizing the expected return at any given level of risk (Fabozzi, 2004, pp.70). The space bounded by the curve BVAZ is the region of possible business opportunities for the set of portfolio combination represented. However, investor would prefer portfolio sets that lies along curve BV because they have a higher rate of return at a lower level of risk. There is no alternative portfolio having lower risk level that exists except the set at point V and therefore it is referred to as the minimum variance portfolio. Plotting the two minimum variance frontiers The following diagram represents the risk- return space diagram for the two-variance frontiers. Figure 1: A space diagram representing the minimum variance for both with and without short sales. As shown in the diagram, for a portfolio with restricted short selling, the upper boundary would be longer than A, specifically at infinity. In the same way, an investor can short sell the highest return security and reinvest the proceeds into the lower yielding asset. For the frontier with unrestricted short selling, the infinitely negative return can be achieved and therefore removing the lower boundary of the efficient frontier. Therefore, short selling increases the range of alternative investments. Question 4 Exchange-traded Funds Exchange-trust fund is a security that is similar to a mutual fund that usually trades in the stock exchange market. Most of the ETFs track the changes of major indices of or industry subsectors. Thus, giving the investors entire exposure to the market of single purchase. ETFs strives to replicate the performance of their standard indices either by holding the indices of the security or by negotiating swap agreements.in spite of the fact that Exchange-traded funds are designed to replicate their standard indices, no of them can be able to do that. Therefore tracking changes in their performance becomes necessary. The two basic methods of tracking the performance of ETFs are tracking difference and the tracking error. Redemption or creation processes and replication methodology are the two basic reasons a slight difference exist between the ETFs’ returns and the standard indices’ returns. Chu (2011) and Frino & Gallagher (2001) argue that the expense ratios are the main sources of tracking error. The expense ratio is a measure of the cost incurred by an investment company that is operating a mutual fund. The ratio is computed annually where the annual funds’ operating expenses are divided by the average dollar value of the assets under management. Experimental observations have previously indicated that there is a negative correlation between tracking error and expense ratio and therefore large tracking errors are produced by funds with higher expense ratio. Tacking error measures how fast the differences between the ETFs and the benchmark index’s returns occurs and therefore total expense ratio has no effect on the tracking error. Tracking error is not affected by the expense ratio because the total tracking ratio does not change throughout the period over which it was calculated (Johnson et al., 2013, pp. 45) There are two main types of ETFs; the physical and synthetic ETFs. ETFs whose objective is to replicate the index synthetically with use of derivatives are referred to as the synthetic ETFs while those who that strive to replicate the index through purchase of shares are called physical ETFs. Replication methodology has a major effect on the tracking performance. Johnson et al., reasons that due to the fact that ETFs using synthetic replication rarely incurs dividends and trading cost, a better tracking performance can be obtained by using the synthetic replication than using the physical replication. Mateus and Rahmani (2014) found that although the average correlation between the ETFs and their benchmark indices returns was 79%, there were significant differences average the sampled period as well as the different categories. The highest correlation coefficient was shown by ETFs that were listed on the London Stock Exchange that provided an exposure to the UK market (with 94%) while ETFs tracking indices of non UK securities exhibited lower correlation returns with their standard indices. The least correlation coefficient was from the Asia Pacific region with 60%. This depicts that there is a strong correlation between the U.K ETFs and their standard indices’ returns. These findings were in agreement with those of Buetow and Herdeson (2012) where they found that the median correlation of United States ETfs that track indices of US securities is 98% while that of US ETFs tracking indices of non-US securities is 72%. The difference in time zones between the UK and non-UK may provide an acceptable explanation of the lower correlation between the non-UK returns and their benchmark indices. The regression analysis results of the ETFs returns against their standard indices returns indicated that at one percent level, the estimated beta coefficients are statistically significant with the average across all observations being 0.84. The largest coefficient was from the UK ETFs with 0.91 while the lowest was from Asia Pacific with 0.70. The findings were consistent with those of Shin and Soydemir (2010), and Buetow and Henderson (2012). For example in Buetow and Henderson (2012), the median beta was 0.94, the largest was from the US. ETFs that had an exposure to the US. equity market (0.96) while the lowest betas was form the US. ETFs tracking indices of non-US securities (0.89) In conclusion, evidence has proved that ETFs with a synthetic replication does not indicate a better daily performance in comparison with ETFs with physical replication. The average expense ratio of physical ETFs were lower than those of synthetic ETFs. This therefore contradicts previous studies about physical and synthetic ETFs. Form the date above, it is evident that SYSCO stock is overvalued and therefore should be avoided or disposed by selling if it is already owned. The intrinsic value of Cinta is higher than the current stock price and therefore t should be purchased or held if it is already owned References Anderson, N. and Sleath J., New estimates of the UK real and nominal yield curves, Bank of England Quarterly Bulletin, (1997), pp 384-96. Asquith P., Andrea S., Thomas R. Covert, Parag A. The Market for Borrowing Corporate Bonds. National Bureau of Economic Research, Paper No. 16228. Blume, M., and Edelen, R. S&P 500 Indexers, Tracking Error, and Liquidity. The Journal of Portfolio Management, Vol. 30, No. 3 (2004), pp. 37-46 Broadie M., Computing Efficient Frontiers using Estimated Parameters. 1993, Vol.45 (1993), No.1, pp 21-58 Chu, P., K. Study on the Tracking Errors and their Determinants: Evidence from Hong Kong Exchange Traded Funds. Applied Financial Economics Vol.21 No.5 (2011), pp.309 – 315 Chua, D., Kritzman, M., and Page, S. “The Myth of Diversification.” The Journal of Portfolio Management, Vol. 36, No. 1 (2009), pp. 26-35. Fabozzi J. F., Short Selling: Strategies, Risks and Rewards. New Jersey; John Wiley & Sons Inc. (2004) Frino A, and Gallagher R. Tracking S&P 500 Index. Journal of Portfolio Management, Vol.28, 1: pp.44-55 Hernderson J. B., and Buetow G., Are Flows Costly For ETF Investors? Journal of Portfolio Management Vol.29, No.2 (2014), pp.71-75. Markowitz, H. Portfolio Selection. Journal of Finance, Vol. 7, No. 1 (1952), pp. 77-91 Minton, B. An empirical examination of basic valuation models for plain vanilla U.S. interest rate swaps, Journal of Financial Economics, Vol.44 (1997), pp 251-77. Pennathur, A., K., Delcoure, N., Anderson, D. (2002) ‘Diversification Benefits of Shares and Close-End Country Funds. Journal of Financial Research. Vol.25, No.4 :( 2002), pp.541 – 557, Shin, Sangheon and Soydemir, and Gokce,. Exchange-Traded Funds, Persistence in Tracking Errors and Information Dissemination. Journal of Multinational Financial Management, Vol. 20, Nos. 4-5, (2010). Read More