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05model 9/16/2011 15:01 12/2/2002 Chapter 5. Model for Analyzing Risk and Rates of 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 30% 100% 20% Normal 40% 15% 15% Weak 30% -70% 10% 100% 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. Electric company's products demand occurring Rate of Return Product Rate of Return Product Strong 30% 100% 30% 20% 6% Normal 40% 15% 6% 15% 6% Weak 30% -70% -21% 10% 3% 100% EXPECTED RATE OF RETURN, k 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 k hat Squared deviation Sq Dev * Prob. company's products demand occurring Martin Products Strong 30% 85% 72.25% 21.68% Normal 40% 0% 0.00% 0.00% Weak 30% -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 Probability of this demand occurring U.S. Electric Strong 30% 5% 0.25% 0.08% Normal 40% 0% 0.00% 0.00% Weak 30% -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 A B C D E F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
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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.
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