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Unformatted text preview: on around the expected value. The expected value of a return, k /^r, is the most likely return on an asset. It is calculated as follows: 26 Risk measurement Risk measurement Here ri is the return if outcome i occurs, Pi is the probability that outcome i occurs, and n is the number of possible outcomes. Thus,^r is a weighted average of the possible outcomes (the ri values), with each outcome’s weight being its probability of occurrence. 27 Expected values of Return for Assets A and B Expected values of Return for Assets A and B 28 Risk measurement Risk measurement The expected values of returns for Norman Company’s assets A and B are presented in the above table . Column 1 gives the Pi’s and column 2 gives the ri’s. In each case n equals 3. The expected value for each asset’s return is 15%. The expression for the standard deviation of returns In general, the higher the standard deviation, the greater the risk. 29 The Calculation of the Standard Deviation of the Returns for Assets A and B 30 Exercise for Practice Rate of Return(%) 6 8 10 12 14 16 18 Asset A Asset B 0.05 0.10 0.20 0.30 0.20 0.10 0.05 0.00 0.25 0.50 0.25 0.00 0.00 0.00 The Normal Probability Distribution 32 Bell­shaped Curve 33 The Normal Probability Distribution The normal probability distribution is a symmetrical, bell­shaped curve. Because it is symmetrical—one side is a mirror image of the other—half of the curve’s area lies to the right of the mean and half to the left. This implies that there is a 50 per cent probability that the actual value will be more than the mean (i.e. lie to the right of the mean value) and a 50 per cent probability that it will be less than the mean (i.e. lie to the left of the mean value). 34 The Normal Probability Distribution As noted on the figure, for normal probability distributions, 68 percent of the possible outcomes will lie between 1 standard deviation from the expected value, 95 percent of all outcomes will lie between 2 standard deviations from the expected value, and 99 percent of all outcomes will lie bet...
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