金融學概论讲义(北大光华管理学院)lecture04.doc

Principles of Finance Lecture 04 Portfolio Theory Probability Distribution of Returns ? Returns on investment are uncertain (risky) ? We model uncertainty of future returns using Expected return: the return you expect to receive on average Volatility (standard deviation): degree of dispersion of future returns The larger a stock’s volatility, the wider the range of possible outcomes and the larger the probabilities of those returns at the extreme of the range  Expected Return : Expected rate of return for investment : Probability of occurrence of ith state : Estimated rate of return for that state n: Number of possible states Example of Calculating Expected Return State of Economy Probability Return on Risco Return on Genco Strong 0.20 50% 30% Normal 0.60 10% 10% Weak 0.20 ?30% ?10% Variance and Standard Deviation Variance for Risco: State of Economy Probability Return Deviation from mean Squared Deviation Probability ? Squared Deviation Strong 0.20 50% 40% 0.16 0.032 Normal 0.60 10% 0 0 0 Weak 0.20 ?30% ?40% 0.16 0.032 and  Risk and Return Revisited I know some statistics…If my investment horizon is long enough, does it mean that I should choose the one with higher expected return, regardless of its higher volatility? (Perhaps in the end I will probably hit a high end-of-period wealth) No. Imagine a scenario like this: a 1% chance of earning $1 billion, and a 99% chance of losing everything. You have a high expected return, but you will be bankrupt with almost certainty! Portfolio Return and Risk State of Economy Probability Return on A Return on B 1 0.20 ?5% 19% 2 0.60 10% 10% 3 0.20 35% ?4% Portfolio weight: and Portfolio Return and Risk State of Economy Prob. Return on A Return on B Portfolio Return 1 0.20 ?5% 19% 4.6% 2 0.60 10% 10% 10% 3 0.20 35% ?4% 19.4% 12% 9% 10.8% 0.6*12%+0.4*9%=10.8% Portfolio return is a weighted average of security returns Portfolio R