tailieunhanh - Seventh Edition - The Addison-Wesley Series in Economics Phần 3

Tính Độ lệch chuẩn của Returns Mức độ rủi ro hoặc không chắc chắn trả về một tài sản cũng ảnh hưởng đến nhu cầu về tài sản. Hãy xem xét hai tài sản, cổ phần trong hãng hàng không Fly-by-Night và cổ phiếu trong Feet-on-theGround Công ty xe buýt. | Models of Asset Pricing 2 p2 probability of occurrence return 2 1 .33 R2 return in state 2 8 Thus Re Calculating Standard Deviation of Returns The degree of risk or uncertainty of an asset s returns also affects the demand for the asset. Consider two assets stock in Fly-by-Night Airlines and stock in Feet-on-the-Ground Bus Company. Suppose that Fly-by-Night stock has a return of 15 half of the time and 5 the other half of the time making its expected return 10 while stock in Feet-on-the-Ground has a fixed return of 10 . Fly-by-Night stock has uncertainty associated with its returns and so has greater risk than stock in Feet-on-the-Ground whose return is a sure thing. To see this more formally we can use a measure of risk called the standard deviation. The standard deviation of returns on an asset is calculated as follows. First calculate the expected return Re then subtract the expected return from each return to get a deviation then square each deviation and multiply it by the probability of occurrence of that outcome finally add up all these weighted squared deviations and take the square root. The formula for the standard deviation Ơ is thus e 2 e 2 e 2 Ơ p1 R1 R I p2 R2 R I . . . pn Rn R 2 The higher the standard deviation Ơ the greater the risk of an asset. EXAMPLE 2 Standard Deviation What is the standard deviation of the returns on the Fly-by-Night Airlines stock and Feet-on-the-Ground Bus Company with the same return outcomes and probabilities described above Of these two stocks which is riskier Solution Fly-by-Night Airlines has a standard deviation of returns of 5 . ơ Vp1 R1 - Re 2 p2 R2 - Re 2 Re P1R1 P2 R2 where p1 probability of occurrence of return 1 2 R1 return in state 1 15 p2 probability of occurrence of return 2 2 R2 return in state 2 5 Re expected return 3 Appendix 1 to Chapter 5 Thus Ơ V - 2 - 2 Ơ V .