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FM12 Ch 06 Tool Kit

# FM12 Ch 06 Tool Kit - Chapter 6 Tool Kit for Risk Return...

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2/1/2007 Chapter 6. Tool Kit for Risk, Return, and the Capital Asset Pricing Model INVESTMENT RETURNS (Section 6.1) Amount invested \$1,000 Amount received in one year \$1,100 Dollar return \$100 Rate of return 10% STAND-ALONE RISK (Section 6.2) 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 Sale.com Basic Foods Strong 0.30 100% 40% 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 Sale.com Basic Foods company's products demand occurring Rate of Return Product Rate of Return Product 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.

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Strong 0.3 100% 30% 40% 12% 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 Demand for the Probability of this Deviation from r hat Squared deviation Sq Dev * Prob. company's products demand occurring Sale.com 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 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 Sale.com's returns.
Probability of this demand occurring Basic Foods Strong 0.3 25% 6.25% 1.88% Normal 0.4 0% 0.00% 0.00% Weak 0.3 -25% 6.25% 1.88% 3.75% Std. Dev. = Square root of sum 19.36% Sq. root can be 19.36% found in two ways USING HISTORICAL DATA Realized Year return 2005 15% 2006 -5% 2007 20% Average =AVERAGE(C68:C70) = 10.0% Standard deviation =STDEV(C68:C70) = 13.2% 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 Sale.com 65.84% 15% 4.39 Basic Foods 19.36% 15% 1.29 The expected return on a portfolio is simply a weighted average of the expected returns of the individual assets in the portfolio.

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