文档介绍：: .
Chapter 1return on the stock is
m – s 2/2 not m
股票的期望收益率为m – s 2/2 ，而不是m
这是因为
ln[E(ST / S0 )] and E[ln(ST / S0 )]
不相同
6m and m −s 2/2
m is the expected return in a very short time, Dt,
expressed with a compounding frequency of Dt
m是很短一段时间Dt内的期望收益率，复利频率为Dt
m −s2/2 is the expected return in a long period of time
expressed with continuous compounding (or, to a
good approximation, with a compounding frequency
of Dt)
m −s2/2是较长一段时间的期望收益率，用连续复利表
示
7Mutual Fund Returns
共同基金收益率 (Business Snapshot on page 304)
Suppose that returns in successive years are 15%, 20%, 30%,
−20% and 25% (ann. comp.)
假设连续五年的年收益率为15%，20%，30%，-20%，25%
The arithmetic mean of the returns is 14%
收益率的算数平均数为14%
The returned that would actually be earned over the five years
(the geometric mean) is % (ann. comp.)
5年实际获得的年收益率为（几何平均）%
The arithmetic mean of 14% is analogous to m
算数平均数14%可以类比于m
The geometric mean of % is analogous to m−s2/2
%可以类比于m−s2/2
8The Volatility 波动率
The volatility is the standard deviation of the continuously
compounded rate of return in 1 year
波动率是一年连续复利收益率的标准差
The standard deviation of the return in a short time period
time Dt is approximately
很短一段时间Dt 内收益的标准差近似为
s Dt
If a stock price is $50 and its volatility is 25% per year
what is the standard deviation of the price change in one
day?
如果股票价格为50美元，波动率为每年25%，一天股价变
动的标准差为多少。