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Lecture 1- Part 2. Risk Management and Derivative by Stulz , Ch:2 Expected Return and Volatility. Knowing risk and return of securities and portfolios. A key measure of investors’ success is the rate at which their funds have grown
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Lecture 1- Part 2 Risk Management and Derivative by Stulz, Ch:2 Expected Return and Volatility
Knowing risk and return of securities and portfolios • A key measure of investors’ success is the rate at which their funds have grown • Holding-period return (HPR) of shares is composed of capital gain and dividend • HPR = (P1-Po + Cash Dividend)/Po • This definition assumes end of period returns and ignores re-investment of income
Return Distributions • If the return on a stock is fixed, there will be 100% probability (Certaininty)that the return will be realized, like in bonds and T-bills • In stocks, return is not fixed so the probability of all likely outcomes should be assessed • Probability is the chance that the specified outcome will occur
Probability distribution is the specification of likely outcomes and the probability associated with each outcome • Suppose we expect that PPL can give either 10%, 20% or -5% return. So we have three possible outcomes, if we associate chances of occurrence with each return, then it becomes probability distribution
Expected Return • Expected return is the single most likely outcome from a PD • It is calculated by taking a weighted average of all possible return outcomes • E(R) = ΣRiPi
Variance of Returns (Risk) • Variance of a random variable is a statistical tools that measures how the realization of the random variable are distribute around their expected values • In other words it measures risk • Variance = Σ[Ri-E(R)]2 Pi
Variance of Returns (Risk) Standard Deviation: taking square root of .00600, we get value of 0.077 or 7.7%
Cumulative Distribution Function • The cumulative distribution function of a random variable y specifies, for any number y, the probability that the realization of the random variable will be no greater than y • For POL, a reasonable estimate of the stock return volatility is 9.2% with expected return of 13%, the following table show cumulative distributions functions for different levels of returns
How to Calculate CDF • CDF can easily be calculated with MS Excel • Put the equal sign in a cell = • Open parenthesis and give x value (x means the level of return for which you want cumulative probability) • Then give the mean return value, • Then the standard deviation value • And finally write TRUE and close parenthesis
Interpretation • Taking values from the table in the previous slide, CDF is .59 with the 20% return level • It means that there is 59% probability that return on POL will be less than 20% • An investor has Rs.100,000 investment in POL and he wants that he does not lose more than Rs.30000 of his investment, what is the probability of this occurrence
Return of a Portfolio • To calculate an average rate on a combination of stocks, we simply take the weighted average return of all stocks • E(Rp) = Σwi E(Ri) • Wi = Weight of the security in the poftfolio • E(Rp) = The expected return on the portfolio
Calculating portfolio return • Calculating weights: PPL = 20000/60000 = .33 • [FFC = 30000/6000 = .5] [Lucky = 10000/60000 = .16
Calculating Portfolio Risk • Risk of the porftolio is not the weighted average risk of the individual securities • Rather it is determined by three factors • 1.the SD of each security • 2. the covariance between the securities • The weights of securities in the portfolio
Diversification • By combining negatively correlated stocks, we can remove the individual risks of the stocks • Example: Pol face the risk of falling oil prices • PIA face the risk of rising oil prices • By combining these two stocks, reduction in return in one stock due to change in oil price is compensated by increase in return of the other stock • However, all of market risk cannot be eliminated through diversification
Efficient Frontier • Investors should select portfolios on the basis of expected return and risk • A portfolio is efficient if: • 1 it has the smallest level of risk for a given return or • 2. largest return for a given level of risk • To select efficient portfolios, investors should find out all portfolios opportunities set • i.e find out risk and return set for all portfolios
Efficient Frontier • Example given in the Excel File • Steps: • 1. Calculate securities return • 2. calculate portfolio returns • 3. Find portfolio risk • 4. Make different portfolios by changing weights of the securities • 5. Find risk and return of each portfolio developed in step 4 • 6. Plot the risk and return of these portfolios • 7. Find the minimum variance portfolio • 8. Portfolios above the minimum variance portfolios are efficient