July 2003 QUESTION 1 For a single investment, risk is measured by the standard deviation of the probabilit distribution of the expected returns. A portfolio's risk cannot be calculated by way of a simple weighted average of the risk of its individual assets, as some of the riskiness of one asset may be offset by the riskiness of another The corre lation coefficient. a measure of the relation between rates of return on two assets is, therefore, very important in determining the risk of a portfolio QUESTION 2 When an outcome or benefit from an investment opportunity is known with certainty, its probabil ity of occurrence is one, and deviations from that value are not expected. Perhaps the closest opportunity to this situation is a government secur ity, for example, Australian Sav ings Bonds(AsB). If an ASB is held to maturity, the probability of investors not receiving either their interest payments or return of principal is so small that it can be regarded as zero conversely, the probability of earning the promised interest rate is one When an investment is risky, however, it means that the outcome could take on any number of possibilities The likelihood of the occurrence of each outcome is measured by its probability. The probability of each occurring is less than one and greater than zero The expected value or mean outcome/return is a weighted average of the possible outcomes calculated. We weight each outcome ki by the probability of that outcome occurring Pri and then sum of the weighted outcomes k=∑k×P The expected value k is a probability weighted average value for the possible outcomes We regard an event as risky because the exact outcome is not known in ad vance even though each possible outcome and its probability of occurrence is known. We define risk in terms of the variability of the outcomes-the greater the variability the greater the risk To measure risk we use the standard devia tion(or variance) of the returns. This provides with a measure of the variabl ity of the outcomes about mean which reflects probability of each occurring. The formula for standard deviation(of a single asset)is a-∑k-PJuly 2003 QUESTION 1 For a single investment, risk is measured by the standard deviation of the probability distribution of the expected returns. A portfolio’s risk cannot be calculated by way of a simple weighted average of the risk of its individual assets, as some of the riskiness of one asset may be offset by the riskiness of another. The correlation coefficient, a measure of the relation between rates of return on two assets, is, therefore, very important in determining the risk of a portfolio. QUESTION 2 When an outcome or benefit from an investment opportunity is known with certainty, its probability of occurrence is one, and deviations from that value are not expected. Perhaps the closest opportunity to this situation is a government security, for example, Australian Savings Bonds (ASB). If an ASB is held to maturity, the probability of investors not receiving either their interest payments or return of principal is so small that it can be regarded as zero; conversely, the probability of earning the promised interest rate is one. When an investment is risky, however, it means that the outcome could take on any number of possibilities. The likelihood of the occurrence of each outcome is measured by its probability. The probability of each occurring is less than one and greater than zero. The expected value or mean outcome/return is a weighted average of the possible outcomes calculated. We weight each outcome ki by the probability of that outcome occurring Pri and then sum of the weighted outcomes: = =  n i 1 i Pri k k The expected value k is a probability weighted average value for the possible outcomes. We regard an event as risky because the exact outcome is not known in advance even though each possible outcome and its probability of occurrence is known. We define risk in terms of the variability of the outcomes - the greater the variability, the greater the risk. To measure risk we use the standard deviation (or variance) of the returns. This provides us with a measure of the variability of the outcomes about the mean which reflects the probability of each occurring. The formula for standard deviation (of a single asset) is: ( ) n i=1 i 2  k = ki - k Pr