Risk Return and Equity - Assignment Example

Question one Expected return for each investment for the next period. Expected returns Sealy Ltd Expected return Gas Ltd Expected return Space Ltd Expected return -4% -264% -7% -167% -10% -172%   7% 40% 4% 56% 8% 28%   9% 25% 7% 43% 10% 31%   12%   10%   13%                   Standard deviation Sealy Ltd standard deviation Gas Ltd standard deviation Space Ltd standard deviation -4% 6% -7% 6% -10% 9% 7% 2% 4% 2% 8% 2% 9% 1% 7% 1% 10% 1% 12%   10%   13%   Question two It can be observed from the table above that Sealy limited is having ideal investment alternativeness as measured by the return on investment of 9%. The implication is that, the stock for Sealy limited is depicting low risk on return and high value as evaluated by the standard deviation which measures the risk of returns. The impact of this is that, high expected returns and low standard deviation might be ideal because, risk is evaluated by standard deviation which is good for venture alternative to an investor to invest in stock that depict the trait of low risk and high value(Alastair Graham, 2000). 3. Correlation coefficient between Sealy and Gas Sealy Ltd Gas Ltd     Sealy Ltd Gas Ltd -4% -7%   Sealy Ltd 1   7% 4%   Gas Ltd 0.999 1 9% 7%         12% 10%                     The table above shows a correlation of 0.999 which is a strong correlation since, it is close to one. The implication there is a strong correlation between the stock for Gas and Sealy ltd Sealy and Gas and Space Correlation Sealy Ltd Gas Ltd Space Ltd Sealy Ltd Gas Ltd Space Ltd -4% -7% -10% Sealy Ltd 1 7% 4% 8% Gas Ltd 0.99947 1.00000 9% 7% 10% Space Ltd 0.99466 0.99349 1 12% 10% 13% The table above depicts a strong correlation 0.999 between Sealy limited, Gas and space limited. The implication is that the three portfolio investment would be recommended to an investment since, an investor will be guaranteed of high return at low cost of capital(Cloonan, 2015). 4. The expected return and standard deviation of a two-asset portfolio comprised of Sealy and Gas ltd Sealy Ltd Expected return Weight Weighted Returns 7% 40% 62% 25% 9% 25% 38% 10% 12% 65% Gas Ltd Expected return Weight Weighted Returns 4% 56% 57% 32% 7% 43% 43% 19% 10% 99% Portfolio Expected Weighted returns Sealy Ltd  Gas Ltd   Weighted Returns Weighted Returns Portfolio Weighted returns 25% 32% 57% 10% 19% 28% Therefore, portfolio expected returns shall be Sealy Ltd Expected return Weight Weighted Returns Space Ltd Expected return Weight Weighted Returns Portfolio Expected returns 7% 40% 62% 25% 8% 28% 47% 13% 38% 9% 25% 38% 10% 10% 31% 53% 16% 26% 12% 65% 13% 59% Portfolio Standard deviation Sealy Ltd 65.05% Expected return standard deviation Weight Weighted standard deviation 7% 40% 2% 62% 1% 9% 25% 1% 38% 0% Gas Ltd         Gas Ltd standard deviation Weight Weighted standard deviation 4.35% 2.80% 60.9% 2% 6.78% 1.47% 60.9% 1% Portfolio Weighted standard deviation Weighted standard deviation(Sealy Ltd) Weighted standard deviation(Gas Ltd) Portfolio Weighted standard deviation 1.4% 2% 4.5% 0.2% 1% 1.2% Sealy and Space shares Sealy Ltd Expected return Weight Weighted Returns Space Ltd Expected return Weight Weighted Returns 7% 40% 62% 25% 8% 28% 47% 13% 9% 25% 38% 10% 10% 31% 53% 16% 12% 65%     13% 59%     Portfolio Expected returns Sealy Ltd Expected return Weight Weighted Returns Space Ltd Expected return Weight Weighted Returns Portfolio Expected returns 7% 40% 62% 25% 8% 28% 47% 13% 38% 9% 25% 38% 10% 10% 31% 53% 16% 26% 12% 65%     13% 59%       Portfolio Expected returns and standard Deviation Sealy Ltd Expected return standard deviation Weight Weighted standard deviation Space Ltd standard deviation Weight Weighted standard deviation 7% 40% 2% 62% 1% 8% 2% 77% 2% 9% 25% 1% 38% 0% 10% 1% 77% 1% Weighted standard deviation(Sealy Ltd) Weighted standard deviation(Space Ltd) Portfolio Weighted standard deviation 1% 2% 3.3%% 0% 1% 1% Gas and Space shares Portfolio Expected Returns Gas Ltd Expected return Weight Weighted return 4% 56% 57% 32% 7% 43% 43% 19% 10% 99%             Space Ltd Expected return Weight Weighted return 8% 28% 47% 13% 10% 31% 53% 16% 13% 59%             Portfolio Weighted Returns       Gas Ltd 32%       19%     Space Ltd         13%       16%     Portfolio Weighted Returns 80%     Portfolios Standard Deviation Space Ltd Standard Deviation Weight Weighted Standard Deviation 7.50% 2.07% 76.60% 2% 9.60% 1.47% 76.60% 1% 12.54% Gas Ltd Standard Deviation Weight Weighted Standard Deviation 4.35% 2.80% 60.90% 2% 6.78% 1.47% 60.90% 1% 11.13% Portfolio Standard Deviation Space Ltd 2% 1% Gas Ltd 2% 1% Portfolio Standard Deviation 6% It is evident from the table above that the investor must hold a diversified efficient portfolio in order to minimize risk and improve the return on investment. The table depicts that holding a portfolio of security would lead to a reduction in risk to 6% as measured by the standard deviation and increase in returns of 80% as compared to having a single portfolio. As a result, to make profit on investment, an investor need to be certain that he hold a portfolio of securities in order to reduce the risk and improve the return on securities(Tom K. Lloyd, 2013). 5. The expected return and standard deviation of a three-asset portfolio comprised of Sealy, Gas and Space shares Sealy Ltd Gas Ltd Space Ltd Expected Return 7% 4% 8% 191% 9% 7% 10% Standard Deviation 12% 10% 13% 0.01 It is evident in the table above that a mix of securities for Sealy, Gas and Space limited creates high return of 191% and low risk as measured by standard deviation of 1% which justifies the need for investing in portfolio combination of securities or assets. This would mean that the growth in investment diversification depicts an inverse relationship with risk of the return(Michael Ehrhardt, 2008). 6. the average return, variance and standard deviation for Air Technologies Ltd, Mineral Resources Ltd and the Market index Standard deviation= {square root of variance}   Average Return Variance Standard Deviation Air Technologies Ltd (%) 3 36 6 Share Market index (%) 3 36 6 Mineral Resources Ltd (%) 3 41 6 7. Systematic risk (Beta) of both Air Technologies and Mineral Resources Ltd. Beta=COVARIANCE.P (equity price array, index price array)/VAR.P (index price array) Month Share Market index (%) Air Technologies Ltd (%)   Mineral Resources Ltd (%) 1 5.08 2.37 2.05 2 5.08 1.37 Beta for Air tech 4.9 Beta for Mineral ltd 3 5.5 1.3 22 -1.5 18 4 1.19 7.71 Slope 7.37 slope 5 -1.79 -1.14 0.59 -7.26 0.80 6 -1.62 -1.51 -3.7 7 -1.13 -6.29 -6.42 8 5.09 3.88 9.87 9 -8.1 -5.26 -3.47 10 2.84 1.61 3.17 11 1.7 2.12 5.12 12 2.74 5.9 8.58 13 6.03 10.83 8.81 14 5.71 10.31 9.84 15 8.64 8.37 2.12 16 11 12.64 7.67 17 -2.49 -4.31 -7.72 18 7.9 2.22 12.83 19 -7.25 -8.51 -1.84 20 1.88 3.76 3.44 21 6.17 9.47 1.31 22 -3.67 -5.99 -2.23 23 2.08 8.93 7.42 24 1.56 10.81 2.1 Beta (β) It evaluates the security volatility in relation to market return. beta is deem an important evaluation tool to investors since, it measures the risk of a security and extent to which an investment should be made on a volatile securities to realize high return on investment. Beta evaluates a data set from dispersion about the mean and thus where there is high dispersion would mean, higher standard deviation. The table above depicts that Beta is will be same to the slope of the trend where slope of the linear regression is employed in determining Beta of the returns(Cloonan, 2015). From the calculations above, it can be observed that the Beta for Air technology is 0.59 and for Mineral Resource is 0.59. Both Betas depict a value which is less than one which means that the securities are less volatile in relation to the markets. In this regards, it can be considered the securities are optimal for investment. 8. Using the capital asset pricing model to calculate the required rate of return for both Air Technologies and Mineral resources Ltd The (CAPM) capital asset pricing model is a model that evaluates the risk premium of a stock. The model identifies return that is equivalent to risk to be gaining in a circumstance that the capital markets maintain the equilibrium CAPM formulae is provided below ra = rrf + Ba (rm-rrf) where: rrf = the required rate of return rm = The market expected return Ba = Beta of the security Risk free rate of return is 3% Expected return = {Risk free rate + Beta * (Market Risk Premium)} Air Technologies Ltd (%) CAPM=3%+0.6(2.9-3%) =2.9% Mineral Resource Ltd CAPM=3%+0.81(2.6-3%) =2.7% It is evident from our working that the required return rate of return for Air technologies limits is 2.9% and for Mineral resource limited is 2.7%. the implication is that the stock is good to invest since; it has a higher rate of return on investment(Cloonan, 2015). 9. The present value for both Companies P0= {Dividend last paid/ (required rate of return-growth} Present value for Air technology Growth rate in dividend is worked out using the following formula Growth= {Dn-Dn01)/ (Dn-1} Where Dn-1 is dividend paid last year N is the number of years Air Technologies start Dividend $2.10 End dividend $2.25 Growth rate {2.25-2.1/2.1}= 1.25 Po={$2.25/2.94%-1.25%}=$1.33 Mineral Resource start Dividend $3.00 End dividend $3.22 Growth rate (3.33-3/3) 2.22 Po={$3.22/2.68%-2.2}=$7 Assumption Growth rate will be steady Short financial forest of 6 years Dividend growth rate is steady. Bibliography Alastair Graham, ‎.C., 2000. Cash Flow Forecasting and Liquidity - Page 21. New York. Cloonan, J., 2015. Measures of Portfolio Risk and How You Can Apply Them. Journal of American Association of individual investors. Michael Ehrhardt, ‎.B., 2008. Corporate Finance: A Focused Approach - Page 554. london. Tom K. Lloyd, S., 2013. Successful Stock Signals for Traders and Portfolio. London: Cingage Learning. Weygandt, J.J., 2009. Managerial Accounting: Tools for Business Decision Making. London. Reference list Alastair Graham, ‎.C., 2000. Cash Flow Forecasting and Liquidity - Page 21. New York. Cloonan, J., 2015. Measures of Portfolio Risk and How You Can Apply Them. Journal of American Association of individual investors. Michael Ehrhardt, ‎.B., 2008. Corporate Finance: A Focused Approach - Page 554. london. Tom K. Lloyd, S., 2013. Successful Stock Signals for Traders and Portfolio. London: Cingage Learning. Weygandt, J.J., 2009. Managerial Accounting: Tools for Business Decision Making. London. Read More