rf
(T )
100 P(T )
1
• Effective annual rate（有效年利率）
1 EAR [1 rf (T)]1/T
• Annual Percentage Rates APR n rf (T )
1 EAR [1 rf (T)]n [1 rf (T)]1/T [1T APR]1/T
The money supply of China
• Interest and inflation rates, 1926–2009
Risk and Risk Premiums（风险溢价）ห้องสมุดไป่ตู้
• Holding-Period Returns（持有期收益率）
• Expected Return and Standard Deviation
• skew
• 中航资本日收益率偏度=-10.1229 • Kurtosis（峰度）
• The Equilibrium Nominal Rate of Interest • Irving Fisher (1930): the nominal rate ought to
increase one-for-one with increases in the expected inflation rate.
• Expected Returns and the Arithmetic Average
E(r) n p(s)r(s) 1 n r(s)
s 1
n s1
p(s) 1 n
• The Geometric (Time-Weighted) Average Return(
几何（时间加权）平均收益）
• g ： the time-weighted (as opposed to dollarweighted) average return,
R r E(i)
• Taxes and the Real Rate of Interest
R(1 t) i (r i)(1 t) i r(1 t) it
Comparing Rates of Return for Different Holding Periods(持有期利率）
• Return rate
APR (1 EAR)T 1 T
• Continuous Compounding（连续复利）
1+EAR exp(rcc ) ercc
rcc ln(1 EAR)
Bills and Inflation, 1926–2009
• Nominal and real wealth indexes for investments in Treasury bills, 1968–2009 (inset figure is for 1926– 2009)
The Normal Distribution
• The normal distribution with mean 10% and standard deviation 20%.
• 中航资本日收益率累计分布
• 中航资本日收益率正态分布概率图
• 中航资本日收益率的密度函数与频率直方图
Deviations from Normality and Risk Measures
Introduction
• What are we refer to , when we discuss the risk? • Uncertainty • The return • How to depict the risk • How to calculate • Calculation method
E(r) p(s)r(s)
s
2 p(s)[r(s) E(r)]2
s
• Risk-free rate（无风险收益率） • Risk premium（风险溢价） • Excess return（超额收益） • Risk aversion（风险厌恶）
Time Series Analysis of Past Rates of Return
Determinants of the Level of Interest Rates
• The main determinants
Business
Households
Reserve bank
The system case-- nonfarm payrolls (非农数据)
• Nonfarm Payroll • A statistic researched, recorded and reported by the
• Discrepancy between the arithmetic and geometric averages
• Variance and Standard Deviation
2 1
n
[r(s) r]2
n s1
1
n
[r(s) r]2
n 1 s1
• The Reward-to-Volatility (Sharpe) Ratio（夏普比率）
• Real and Nominal Rates of Interest • A promised rate of return • Unit • Time period
• Real interest rate r R i
1 r 1 R 1 i
r Ri 1 i
• Determination of the equilibrium real rate of interest
U.S. Bureau of Labor Statistics intended to represent the total number of paid U.S. workers of any business, excluding the following employees:
- general government employees - private household employees - employees of nonprofit organizations that provide assistance to individuals - farm employees