Quantitative Analysis for Finance - Coursework Example

Quantitative Analysis for Finance al affiliation: The main focus of these three exercises include calculation of the return on the stock, bond and total portfolio of the investors during the year; Determination of the capital market line equation(CML) and calculation of the standard deviation and the expected return of the stock. In regards to the calculations of the return on the stock, bond and total portfolio of the investors during the year, the first step was to calculate the percentage returns of both the stock and the bond portfolio basing on the initial investment of 50000 pounds. The next step was to calculate the percentage of the values of the bonds and stocks after a year were calculated which were 23 000 pounds and 25 000 pounds. Basing on the calculated percentages, the return of each portfolio was calculated. Therefore, based on the results, the plan consists of the losses and the highest drawdown which could help investors prepare for what they could face in future. In relation to this, even if the financial plan is considered to be the simplest, it needs assumptions about the way the investment could perform. It is known that such assumptions might not be accurate, but they are required to be reasonable as well as thoughtful. The projections won’t be that useful in case you assume a balanced portfolio with a return of 7 percent every day. It was found that the returns of the total portfolio of investors during the year are negative and this indicates that the portfolio is not good enough to invest. Such resulted from the drop in value of the initial investment of the common bond which was from 30 000 pounds to 23 000 pounds. There was rise in value of the stock investment from 20 000 pounds to 25 000 pounds and this implies that the stock portfolio is good for investment. In regard to the determination of the capital market line equation (CML), we considered the fact that there was a correlation coefficient between the stock returns of 30 percent and the risk free rate of 5 percent .The risk profile could be altered easily when the asset risk is adjusted with the use of the risk –free rate. Based on the capital market line, the market portfolio has a combination of all risky-free asset and risky assets, with the use of the asset‘s market value to calculate the weights. The capital market line was derived by capital market model (CAPM) where the expected return at different risk levels was solved. For exercise 2, the capital market line was determined and in this case, it indicated that the diversified portfolio returns on the capital market line is equal to risk free rate together with the risk premium. The capital market line equation conclusion is that higher returns need additional risk. For exercise 3 it was required to calculate the expected returns as well as the standard deviations of the stock. The first step was to estimate the weighed returns then get the total which was now the expected return. Introduction A bond is considered to be a debt instrument where the borrower promises to pay back a particular amount of money at a given future date (Painter 2010). The money to be paid back has two components that include the principal and interest. For instance, the issuer or borrower has responsibility of paying the interest at a fixed rate two times every year as well as the principal upon the maturity date. The principal which is the amount to be paid by the borrower to the lender is as well referred to as the par value or face value (Sharp 2000).The interest rate for a bond is referred to as a coupon. The coupon rate can be termed as the interest rate which is expressed in principal percentage. Since the coupon payments are not distributed by the bond issuer on a daily basis the seller must be paid by the bond buyer for the earned interest and this is referred to as accrued interest. The buyer is required to pay the seller the amount agreed upon the transaction. The market price is usually not observable since the transaction of the bonds is not on a daily basis. Therefore, in order to calculate the daily returns of the bonds, the evaluated price could be considered and it is the theoretical fair bond price Even the financial plan that is the simplest needs assumptions about the way the investment could perform. It is known that such assumptions might not be accurate, but they are required to be reasonable as well as thoughtful. The projections won’t be that useful in case you assume a balanced portfolio with a return of 7 percent every day (Xuemei and Xinshu 2003). The question posed could be what the reasonable assumption for bonds and stocks is. There are two methods which could be applied to estimate the future returns and they include relying on the history; for instance, if the global stocks average return was 8 percent for the past century, it could be assumed that the same is moving forward. The second method applies valuation metric in estimating the future stock returns basing on the conditions of the current market. These two methods could as well be applied to the expected bond returns with the use of either the current yield on a benchmark or the long term historical average (Xuemei and Xinshu 2003). All efficient portfolio are based on the efficient frontier, but incase an efficient portfolio has only the risky asset in combination with a risk-free asset, then the efficient portfolio will cease from lying on the efficient frontier that is curved. In this case, when the risky asset and risk free asset portfolio are combined there will be an enhanced linear efficient frontier and it is referred to as capital market line (CML) (Xuemei and Xinshu 2003).There will be one capital market line theoretically. The capital market line is known to intercept the vertical axis which is the expected return at point (Rf) which could be the risk free rate and this has been illustrated in the below figure. The capital market line later extends to a point where the capital market line is tangent to the efficient frontier referred to as market portfolio which consists of all the risky assets. The market portfolio has all the non-systematic risk which is only systematic risk that has been diversified away (Xuemei and Xinshu 2003). A direct correspondence does exist between the risk-free asset proportion and risky assets in the risk portfolio and the portfolio of the investor. For instance, in case the portfolio of the investor has risk-free assets of 50% and 50% risky assets, the portfolio risk of the investor of 50% of the standard deviation of the market portfolio; in case the portfolio of the investor has 20% risk free assets as well as 80% risky assets (LeRoy and Werner 2001). Then the capital market equation will be The above indicates that the diversified portfolio returns on the capital market line is equal to risk free rate together with the risk premium. The capital market line equation conclusion is that higher returns needs additional risk. In case the portfolio and market standard deviation are equal, then they will cancel each other and the portfolio return is the risk free rate and the market risk premium (rm-rf) Source: (Xuemei and Xinshu 2003) Calculations and interpretations Exercise 1 a) The return on the investor’s stock portfolio during the year Initial investments=20000 A year later value =25000 Interest rate=1000 Return = ((25000-20000)*100)/20000 =25% The return on the investor’s stock portfolio during the year is 25% b) The return on the investor’s bond portfolio during the year Initial investments=30000 A year later value =23000 Interest rate=1000 Return = ((23000-30000)*100)/30000 =-23% Therefore, the return on the investor’s bond portfolio during the year is -23% c) The return on the investor’s total portfolio during the year =Weight x expected returns Weights for bond portfolio= 30000*100/50000 = 60% Weight for stock portfolio =20000*100/50000 =40% Therefore the return on the investor’s total portfolio is: 60x-23+ 40x25= -3.8% Therefore, the return on the investor’s total portfolio during the year is -3.8% Exercise 2 The market portfolio has 40% of stock A and 60% of stock B The expected return of A=10% The expected return of B=15% The standard deviation of the return of A =20% The standard deviation of B =28% The correlation coefficient between the stock returns =30% Risk free rate =5% Basing on the above the capital market equation can be determined as: We use the below equation to derive the required equation We first calculate the portfolio returns: = 40x10+ 15x60 =13% The portfolio return now is 13% We then calculate the standard deviation of the portfolio: 28x40 +60x20=23.2% The standard deviation of the portfolio is 23.2% Using the above calculations, the capital market equation is as: Exercise 3 The investment is for one year and the probability distribution of returns for the stock were estimated under five probable economy states over the next year. Basing on these estimates, we are required to calculate the expected returns as well as the standard deviations of the stock. State of the economy Return Probability Weighed return 1 -10% 0.1 -1 2 0% 0.25 0 3 10% 0.4 4 4 20% 0.2 4 5 30% 0.05 1.5 Expected return 8.5 STDEV 3.444802849 The expected return is: = 8.5% Therefore, the standard deviation is the square root of the variance =3.44 The standard deviation of the stock is 3.447 Conclusion and recommendation The main focus of these three exercises include calculation of the return on the stock, bond and total portfolio of the investors during the year; Determination of the capital market line equation(CML) and calculation of the standard deviation and the expected return of the stock. In regards to the calculations of the return on the stock, bond and total portfolio of the investors during the year, it was found that the returns of the total portfolio of investors during the year is negative and this indicates that the portfolio is not good enough to invest. Such resulted from the drop in value of the initial investment of the common bond which was from 30 000 pounds to 23 000 pounds. There was rise in value of the stock investment from 20 000 pounds to 25 000 pounds and this implies that the stock portfolio is good for investment. For exercise 2, the capital market line was determined and in this case, it indicated that the diversified portfolio returns on the capital market line is equal to risk free rate together with the risk premium. The capital market line equation conclusion is that higher returns need additional risk. For exercise 3 it was required to calculate the expected returns as well as the standard deviations of the stock. The first step was to estimate the weighed returns then get the total which was now the expected return. It is pertinent to note that the capital market line never specify the risk relationship of the inefficient portfolios or individual securities. In case the portfolio of the investor lies on the capital market line beyond or starting at the market portfolio, the portfolio of the investor has only risky asset (Painter 2010). A planner who is responsible is required to make sure that the customer is able to understand that in case they invest 60 percent bond and 40 percent stocks they should expect to face an annual decline of 15 percent as well as a maximum drawdown of over 23 percent .The reason to this is that such is seen to happen more often (Sharp 2000). Therefore, based on the results, the plan consists of the losses and the highest drawdown which could help investors prepare for what they could face in future. In relation to this, even if the financial plan is considered to be the simplest, it needs assumptions about the way the investment could perform. It is known that such assumptions might not be accurate, but they are required to be reasonable as well as thoughtful. The projections won’t be that useful in case you assume a balanced portfolio with a return of 7 percent everyday (Sharp 2000). References Painter, M. J., (2010). the portfolio diversification impact of a farmland real estate investment trust, International Business & Economics Research Journal, Vol. 9, No. 5, pp. 115-123, , Sharp, W. F. (2000). “Portfolio Theory and Capital Markets”, New York, McGraw-Hill,. Xuemei, A. and Xinshu, (2003). The identifying of the efficient market portfolio, Chinese Business Review, Vol. 2, No. 5, pp. 70-75 ,. LeRoy, S. F. and Werner, J. (2001). “Principle of Financial Economics”, Cambridge: Cambridge University Press.. Read More