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投资回报率 投资风险的衡量 期望收益率 标准差 风险价值 投资组合的风险 ●Investment Return The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return = __________________________________ Amount invested sweee For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%. ●Investment Risk 投资风险 Definition 定义 Two types of investment risk:Stand-alone risk;Portfolio risk Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment. Probability distributions 概率分布与期望收益率 A listing of all possible outcomes, and the probability of each occurrence. Can be shown graphically. So,we can use this to calculate the expected return for each alternative. E.g. KA= 0.3×20%+0.4× 15%+0.3× 10%=15% KB= 0.3×100%+0.4× 15%+0.3× (-70%)=15% Standard deviation for each alternative 标准差 Standard deviation (σi) measures total, or stand-alone, risk.It shows the weighted average of deviation between all possible and expected value.So it can tell people the actual value may how much higher or lower than expected value. The larger σi is, the lower the probability that actual returns will be closer to expected returns. Larger σi is associated with a wider probability distribution of returns. Only if two company’s return are same,we can use this way to measure the risk. Coefficient of Variation (CV) 标准差率 A standardized measure of dispersion about the expected value, that shows the risk per unit of return.We can also use CV to measure the risk,especially when two investment’s expected return are same. E.g 项目 投资C 投资D 期望收益 0.08 0.24 标准差 0.06 0.08 标准差率 0.75 0.33 ●Value at Risk 风险价值 Investors take risk to investment,so they ask for extra money which is beyond the time value.And the extra money is value at risk. Why ask more? Risk aversion风险反感– assum