Ch_03_Tool_Kit - Ch 03 Tool Kit Chapter 3 Tool Kit for Risk...

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Ch 03 Tool Kit 5/26/2002 Chapter 3. Tool Kit for Risk and Return The relationship between risk and return is a fundamental axiom in finance. Generally speaking, it is totally logical to assume that investors are only willing to assume additional risk if they are adequately compensated with additional return. This idea is rather fundamental, but the difficulty in finance arises from interpreting the exact nature of this relationship (accepting that risk aversion differs from investor to investor). Risk and return interact to determine security prices, hence its paramount importance in finance. PROBABILITY DISTRIBUTION The probability distribution is a listing of all possible outcomes and the corresponding probability. Demand for the Probability of this Rate of Return on stock company's products demand occurring if this demand occurs Martin Products U.S. Water Strong 0.30 100% 20% Normal 0.40 15% 15% Weak 0.30 -70% 10% 1.00 EXPECTED RATE OF RETURN The expected rate of return is the rate of return that is expected to be realized from an investment. It is determined as the weighted average of the probability distribution of returns. Demand for the Probability of this Martin Products U.S. Water company's products demand occurring Rate of Return Product Rate of Return Product Strong 0.3 100% 30% 20% 6% Normal 0.4 15% 6% 15% 6% Weak 0.3 -70% -21% 10% 3% 1.0 EXPECTED RATE OF RETURN, r hat 15% 15% MEASURING STAND-ALONE RISK: THE STANDARD DEVIATION To calculate the standard deviation, there are a few steps. First find the differences of all the possible returns from the expected return. Second, square that difference. Third, multiply the squared number by the probability of its occurrence. Fourth, find the sum of all the weighted squares. And lastly, take the square root of that number. Let us apply this procedure to find the standard deviation of Martin Products' returns. Demand for the Probability of this Deviation from r hat Squared deviation Sq Dev * Prob. company's products demand occurring Martin Products Strong 0.3 85% 72.25% 21.68% Normal 0.4 0% 0.00% 0.00% Weak 0.3 -85% 72.25% 21.68% Sum: 43.35% Std. Dev. = Square root of sum 65.84% Sq. root can be 65.84% found in two ways
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Probability of this demand occurring U.S. Water Strong 0.3 5% 0.25% 0.08% Normal 0.4 0% 0.00% 0.00% Weak 0.3 -5% 0.25% 0.07% 0.15% Std. Dev. = Square root of sum 3.87% Sq. root can be 3.87% found in two ways MEASURING STAND-ALONE RISK: THE COEFFICIENT OF VARIATION The coefficient of variation indicates the risk per unit of return, and is calculated by dividing the standard deviation by the expected return. Std. Dev. Expected return CV Martin Products 65.84% 15% 4.39 U.S. Water 3.87% 15% 0.26 PORTFOLIO RETURNS The expected return on a portfolio is simply a weighted average of the expected returns of the individual assets in the portfolio. Consider the following portfolio. Stock Portfolio weight Expected Return Microsoft 0.25 12.0% General Electric 0.25 11.5% Pfizer 0.25 10.0% Coca-Cola 0.25 9.5% Portfolio's Expected Return 10.75% PORTFOLIO RISK deviations--usually, it is much lower than the weighted average. The portfolio's SD is a weighted average only if all the securities in it are perfectly positively correlated, which is almost never the case.
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