# Essays on Finance Portfolio Assignment

a) The rate of return (ROR) or return on investment (ROI) is the ratio of money either gained or lost on an investment relative to the amount of money invested. The gained or lost money can be referred to as a profit or a loss respectively, while the money invested are referred to as asset, capital the cost basis or the principal. The rate of return is often expressed in percentage. When calculating the rate of return, we always take the initial value or principal amount subtract it from the final value and then divided by the initial amount.

When the Initial amount is represented with Vi, while Final amount Vf. Then the rate of return can be calculated using the formula; R= {(Vf – Vi)/ Vi}100Therefore rate of return on weekly basis for Waterco ltd are; Feb3101724ROR6%5%0%39%March29162330ROR9%13%30%10%8%April6132027ROR4%13%1%0%May4111825ROR4%9%0%14%June18152229ROR2%29%14%4%8%July6132027ROR25%9%20%25%Aug310172431ROR27%351%6%12%The rate of return on weekly basis for Watpac companyFeb3101724ROR1%0%5%1%March29162330ROR1%2%051%2%April6132027ROR1%0%153%May4111825ROR0%5%0%0%June18152229ROR0%4%1%0%2%July6132027ROR3%1%1%4%Aug310172431ROR0%1%1%353%The rate of return for Aberdeen Leaders Company are; Feb3101724ROR53%24%20%11%March29162330ROR29%26%27%8%24%April6132027ROR55%47%22%30%May4111825ROR44%24%7%1%June18152229ROR9%48%4%2%51%July6132027ROR11%9%29%37%Aug310172431ROR40%14%26%9%4%Part 2Discreet rate of return time moves forward in increment with each increment having a rate of return equal to 1. The more frequent the compounding, the higher the rate of return.

On the other hand, continuous rate of return associated with a holding period is found by taking the natural of 1+holding – period return. Continuous rate of return ln (rate)For the first Friday of every month from February to AugustWaterco ltdMonthFeb 3March2April 6May 4June 1July 6Aug 3Continous RORLN(6) 1.79Ln(9) 2.2Ln(4) 1.3Ln(4) 0.3Ln(2) 0.6Ln(25) 3.2Ln(27) 3.29Watpac companyMonthFeb 3March2April 6May 4June 1July 6Aug 3Continous RORLn(1) 0Ln(1) 0Ln(1) 0Ln(0) 0Ln(0) 0Ln(3) 1.1Ln(0) 0Aberdeen leaders companyMonthFeb 3 March2April 6May 4June 1July 6Aug 3Continous RORln(53) 3.97ln(29) 3.36ln(55) 4.0ln(44) 3.78ln(9) 2.2Ln(11) 2.3Ln(40) 3.86Part 3The variance of returnsThe variance of a portfolio reflects the variance of the stocks that make up the portfolio, it also reflects how the returns on the stocks that comprise the portfolio (Globusz, 2012).

The covariance of a stock is how the returns on a pair or two stocks vary together. The covariance of two stocks can be calculated using the following formula. Cov (R1,R2)={P1(R1i-E[R1])(R2i- E{R2])Where N=number of statesP1=probability stateR1i =return on stockE(R1)=expected return on stock1R2i=return on stock 2 in state iE(R2)= expected return on stock 2Correlation coefficient between the returns on two stocks is calculation by the following formulaeCorr (R1,R2)=Cov (R1,R2)/SD(R1)SD(R2)WhereR12= Correlation coefficient between the returns on stocks 1 and 2SD=the standard deviationRisk return is the gain the investor has got from investing in a number of stocks.

The investors do not risk their investment just only in one stock, they take a portion for each stock so that when a loss happens, they incur a partial loss, and thus they spread the risk. Security characteristic line is a regression line showing the performance of a particular stock portfolio against that of the market portfolio at every point.

Security characteristic line is found by the following formula. SCL: Ri, t –Rf=Xi +Bi (Rm, t –Rf) +Ei, tWhereXi =is the asset of alpha or abnormal returnBi (Rm, t-Rf) is non diversifiable or systematic riskEi is diversifiable idiosyncratic risk