5-1
第 5 章利率史与风险溢价
History of Interest Rates and Risk Premiums
5-2
5.1 利率水平的确定方式
5.2 风险和风险溢价
5.3 历史记录
5.4 真实风险与名义风险
5.5 收益分布和风险价值
5.6 关于历史记录的全球观点
5.7 长期预测利率史与风险溢价
History of Interest Rates and Risk Premiums
5-3
影响利率的因素
Factors Influencing Rates
资金供给 Supply
–居民 Households
资金需求 Demand
–企业 Businesses
政府净供给或净需求 Government’s Net
Supply and/or Demand
–联邦储备银行运作
Federal Reserve Actions
5-4
Q0 Q1
r0
r1
Funds 资金利率 Interest Rates
供给 Supply
Demand 需求利率水平 Level of Interest Rates
5-5
费雪效应,近似
Fisher effect,Approximation
名义利率 =真实利率 +通货膨胀率
nominal rate = real rate + inflation premium
R = r + i or r = R - i
例如 Example r = 3%,i = 6%
R = 9% = 3% + 6% or 3% = 9% - 6%
费雪效应,严格 Fisher effect,Exact
r = (R - i) / (1 + i)
2.83% = (9%-6%) / (1.06)
真实利率与名义利率
Real vs,Nominal Rates
5-6
例如，如果一年期储蓄存单的利率为 8%，预期下一年的通胀率为 5%，利用近似公式可以得到真实利率为
r ＝ 8 % - 5 % ＝ 3 %,
利用精确公式可以计算出真实利率为
r = (0.08 - 0.05)/(1+0.05)= 0.028 即 2.86%。
由此可以看到，近似公式得出的真实利率高估了 14个基点（ 0.14%），通胀率较小或计算连续复利情形时，近似公式较为准确。
真实利率与名义利率
Real vs,Nominal Rates
5-7
P
DPPH PR
0
101
HPR = 持有期收益率 Holding Period Return
P0 = 期初价 Beginning price
P1 = 期末价 Ending price
D1 = 周期 1的现金红利 Dividend during period one
利息收益,单周期
Rates of Return,Single Period
5-8
期末价 Ending Price = 48
期初价 Beginning Price = 40
红利 Dividend = 2
持有期收益率 HPR = (48 - 40 + 2 )/ (40) = 25%
利息收益,单周期举例
Rates of Return,Single Period Example
5-9
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
例如，假定你有一笔钱用于投资，你把它们都投资于银行储蓄帐户和股票指数基金。指数基金每股价格为 100 美元，持有期为一年，你对年现金红利的要求为 4美元,所以你的期望红利收益率（每美元红利收入）为 4%。 你的总持有期收益率（ HPR）取决于你对从现在起一年的基金价格的预期，
假定最好情形下你预期每股价格为 110美元，那么持有期收益为 14%，持有期收益具体是指基金资本收益加上红利收益，
时间基点为期初。
HPR＝ (股票期末价格 -期初价格＋现金红利 )/ 期初价格本例中
110美元 -100美元＋ 4美元
HPR＝ ＝ 0.14或 14%
100美元
5-10
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
For example,suppose you are considering investing some of your
money,now all invested in a bank account,in a stock market index fund,
The price of a share in the fund is currently $100,and your time horizon
is one year,You expect the cash dividend during the year to be $4,so
your expected dividend yield (dividends earned per dollar invested) is
4%,Your total holding-period return (HPR) will depend on the price you
expect to prevail one year from now,Suppose your best guess is that it
will be $110 per share,Then your capital gain will be $10 and your HPR
will be 14%,The definition of the holding-period return in this context is
capital gain income plus dividend income per dollar invested in the
stock at the start of the period:
HPR= (Ending price - Beginning price + Cash dividend) / Beginning
price
In our case we have
HPR = (110-100＋ 4)/100=0.14 (OR 14%)
5-11
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
表 5-1 股票市场总收益率的概率分布经济状况 概率 期末价 /美元 总收益率（ %）
繁荣 0.25 140 44
正常增长 0.50 110 14
萧条 0.25 80 -16
State of the Ending
Economy Probability Price HPR
Boom,25 $140 44%
Normal growth,50 110 14
Recession,25 80 –16
5-12
期望收益 Subjective returns
p(s) = 状态 S的概率 probability of a state
r(s) =状态 S的持有期收益率 return if a state occurs
状态,从 1到 S 1 to s states
均值计算,期望收益
Measuring Mean,Scenario or Subjective Returns
rprE s
s
s?
1
)(
5-13
利用表 5-1中所列数据，我们得到该指数基金的期望收益率为
Applying this formula to the data in Table 5.1,
we find that the expected rate of return on the
index fund is：
E(r)＝ (0.25× 44%)＋ (0.5× 14%)＋ [0.25× (-16%)]＝ 14%
均值计算,期望收益
Measuring Mean,Scenario or Subjective Returns
5-14
标准差 Standard deviation = [方差 variance]1/2
收益的标准差用来测度风险，它是方差的平方根，即期望收益方差的期望值。结果的波动程度越强，这些方差的均值也就越大，所以，方差和标准差可用来测度风险 。
公式为 Subjective or Scenario
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
rErp s
s
s
2
2
5-15
方差 Var =(.25)(44-14)2+(.5)(14-14)2+ (.25)(-16-14)2
方差 Var= 450
标准差 S.D.= [ 450] 1/2 =21.21%
举例 Using Our Example:
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
5-16
显然，对于潜在的投资者而言，更加担心的是收益为 -16%这一情形出现的概率有多大，而不是收益为 44%的这一情形。收益率的标准差并未将两者加以区分，它仅仅简单地表现为是对二者中值的偏离。只要概率分布或多或少与中值是对称的,σ就可以精确测度风险，特别地，当我们假定概率分布为正态分布（即通常的铃形曲线）时,E(r)与 σ就充分准确地体现了概率分布的特点。
Clearly,what would trouble potential investors in the index fund is the
downside risk of a –16% rate of return,not the upside potential of a 44%
rate of return,The standard deviation of the rate of return does not
distinguish between these two; it treats both simply as deviations from
the mean,As long as the probability distribution is more or less
symmetric about the mean,σis an adequate measure of risk,In the
special case where we can assume that the probability distribution is
normal—represented by the well-known bell-shaped curve—E(r)
andσare perfectly adequate to characterize the distribution.
概率分布特性
Characteristics of Probability Distributions
5-17
对称分布 Symmetric distribution
中值 mean
s.d,s.d.
正态分布
Normal Distribution
5-18
风险和风险溢价
Risk and Risk Premiums
回报分为两种：一种是投资于指数基金的期望总收益，一种是投资于譬如国库券、货币市场工具或银行存款上的无风险收益率。两者之差我们称之为普通股风险溢价。如果例中的无风险收益率每年为 6%，指数基金期望收益率每年为 14%，那么股票的风险溢价每年就为 8%。
We measure the reward as the difference between the
expected HPR on the index stock fund and the risk-free rate,
that is,the rate you can earn by leaving money in risk-free
assets such as T-bills,money market funds,or the bank,We
call this difference the risk premium on common stocks,If
the risk-free rate in the example is 6% per year,and the
expected index fund return is 14%,then the risk premium on
stocks is 8% per year,
5-19
年持有期收益率的概率分布
Annual Holding Period Returns
几何平均 算术平均 标准差
Geom,Arith,Stan.
类列 Series Mean% Mean% Dev.%
大公司股票 Lg,Stk 10.51 12.49 20.30
小公司股票 Sm,Stk 12.19 18.29 39.28
长期国家基金 LT Gov 5.23 5.53 8.18
国库券 T-Bills 3.80 3.85 3.25
通货膨胀率 Inflation 3.06 3.15 4.40
5-20
类别 风险溢价 实际收益
Risk Real
Series Premiums% Returns%
Sm Stk 15.0 15.6
Lg Stk 9.3 9.9
LT Gov 1.6 2.2
T-Bills --- 0.6
Inflation --- ---
年持有期风险溢价和实际收益
Annual Holding Period Risk Premiums
and Real Returns
5-21
经济的真实利率的均衡水平由居民储蓄意愿（影响资金供给曲线）和企业投资 固定资产、厂房设备的期望利润率水平（影响需求曲线）决定。此外也受政府财政政策和货币政策的影响。
The economy’s equilibrium level of real interest
rates depends on the willingness of households to
save,as reflected in the supply curve of funds,
and on the expected profitability of business
investment in plant,equipment,and inventories,
as reflected in the demand curve for funds,It
depends also on government fiscal and monetary
policy,
summary
5-22
名义利率等于真实均衡利率加上通胀率。通常，我们只能直接得到名义利率,我们必须通过通胀预期来推断真实利率。
The nominal rate of interest is the
equilibrium real rate plus the expected rate
of inflation,In general,we can directly
observe only nominal interest rates; from
them,we must infer expected real rates,
using inflation forecasts.
summary
5-23
任何证券的均衡期望收益率均由其均衡真实收益率、期望通胀率和证券特别风险溢价三者相加而成。
The equilibrium expected rate of return on
any security is the sum of the equilibrium
real rate of interest,the expected rate of
inflation,and a security-specific risk premium.
summary
5-24
投资者面临着风险 -期望收益权衡的选择。由本章历史数据的分析得出：低风险资产提供低收益，反之亦然。
Investors face a trade-off between risk and
expected return,Historical data confirm our
intuition that assets with low degrees of risk
provide lower returns on average than do
those of higher risk.
summary
5-25
由于未来通胀率的不确定性，保证获得名义利率的资产实际上存在着风险。
Assets with guaranteed nominal interest
rates are risky in real terms because the
future inflation rate is uncertain.
summary
第 5 章利率史与风险溢价
History of Interest Rates and Risk Premiums
5-2
5.1 利率水平的确定方式
5.2 风险和风险溢价
5.3 历史记录
5.4 真实风险与名义风险
5.5 收益分布和风险价值
5.6 关于历史记录的全球观点
5.7 长期预测利率史与风险溢价
History of Interest Rates and Risk Premiums
5-3
影响利率的因素
Factors Influencing Rates
资金供给 Supply
–居民 Households
资金需求 Demand
–企业 Businesses
政府净供给或净需求 Government’s Net
Supply and/or Demand
–联邦储备银行运作
Federal Reserve Actions
5-4
Q0 Q1
r0
r1
Funds 资金利率 Interest Rates
供给 Supply
Demand 需求利率水平 Level of Interest Rates
5-5
费雪效应,近似
Fisher effect,Approximation
名义利率 =真实利率 +通货膨胀率
nominal rate = real rate + inflation premium
R = r + i or r = R - i
例如 Example r = 3%,i = 6%
R = 9% = 3% + 6% or 3% = 9% - 6%
费雪效应,严格 Fisher effect,Exact
r = (R - i) / (1 + i)
2.83% = (9%-6%) / (1.06)
真实利率与名义利率
Real vs,Nominal Rates
5-6
例如，如果一年期储蓄存单的利率为 8%，预期下一年的通胀率为 5%，利用近似公式可以得到真实利率为
r ＝ 8 % - 5 % ＝ 3 %,
利用精确公式可以计算出真实利率为
r = (0.08 - 0.05)/(1+0.05)= 0.028 即 2.86%。
由此可以看到，近似公式得出的真实利率高估了 14个基点（ 0.14%），通胀率较小或计算连续复利情形时，近似公式较为准确。
真实利率与名义利率
Real vs,Nominal Rates
5-7
P
DPPH PR
0
101
HPR = 持有期收益率 Holding Period Return
P0 = 期初价 Beginning price
P1 = 期末价 Ending price
D1 = 周期 1的现金红利 Dividend during period one
利息收益,单周期
Rates of Return,Single Period
5-8
期末价 Ending Price = 48
期初价 Beginning Price = 40
红利 Dividend = 2
持有期收益率 HPR = (48 - 40 + 2 )/ (40) = 25%
利息收益,单周期举例
Rates of Return,Single Period Example
5-9
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
例如，假定你有一笔钱用于投资，你把它们都投资于银行储蓄帐户和股票指数基金。指数基金每股价格为 100 美元，持有期为一年，你对年现金红利的要求为 4美元,所以你的期望红利收益率（每美元红利收入）为 4%。 你的总持有期收益率（ HPR）取决于你对从现在起一年的基金价格的预期，
假定最好情形下你预期每股价格为 110美元，那么持有期收益为 14%，持有期收益具体是指基金资本收益加上红利收益，
时间基点为期初。
HPR＝ (股票期末价格 -期初价格＋现金红利 )/ 期初价格本例中
110美元 -100美元＋ 4美元
HPR＝ ＝ 0.14或 14%
100美元
5-10
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
For example,suppose you are considering investing some of your
money,now all invested in a bank account,in a stock market index fund,
The price of a share in the fund is currently $100,and your time horizon
is one year,You expect the cash dividend during the year to be $4,so
your expected dividend yield (dividends earned per dollar invested) is
4%,Your total holding-period return (HPR) will depend on the price you
expect to prevail one year from now,Suppose your best guess is that it
will be $110 per share,Then your capital gain will be $10 and your HPR
will be 14%,The definition of the holding-period return in this context is
capital gain income plus dividend income per dollar invested in the
stock at the start of the period:
HPR= (Ending price - Beginning price + Cash dividend) / Beginning
price
In our case we have
HPR = (110-100＋ 4)/100=0.14 (OR 14%)
5-11
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
表 5-1 股票市场总收益率的概率分布经济状况 概率 期末价 /美元 总收益率（ %）
繁荣 0.25 140 44
正常增长 0.50 110 14
萧条 0.25 80 -16
State of the Ending
Economy Probability Price HPR
Boom,25 $140 44%
Normal growth,50 110 14
Recession,25 80 –16
5-12
期望收益 Subjective returns
p(s) = 状态 S的概率 probability of a state
r(s) =状态 S的持有期收益率 return if a state occurs
状态,从 1到 S 1 to s states
均值计算,期望收益
Measuring Mean,Scenario or Subjective Returns
rprE s
s
s?
1
)(
5-13
利用表 5-1中所列数据，我们得到该指数基金的期望收益率为
Applying this formula to the data in Table 5.1,
we find that the expected rate of return on the
index fund is：
E(r)＝ (0.25× 44%)＋ (0.5× 14%)＋ [0.25× (-16%)]＝ 14%
均值计算,期望收益
Measuring Mean,Scenario or Subjective Returns
5-14
标准差 Standard deviation = [方差 variance]1/2
收益的标准差用来测度风险，它是方差的平方根，即期望收益方差的期望值。结果的波动程度越强，这些方差的均值也就越大，所以，方差和标准差可用来测度风险 。
公式为 Subjective or Scenario
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
rErp s
s
s
2
2
5-15
方差 Var =(.25)(44-14)2+(.5)(14-14)2+ (.25)(-16-14)2
方差 Var= 450
标准差 S.D.= [ 450] 1/2 =21.21%
举例 Using Our Example:
方差或 期望收益偏差的计算
Measuring Variance or Dispersion of Returns
5-16
显然，对于潜在的投资者而言，更加担心的是收益为 -16%这一情形出现的概率有多大，而不是收益为 44%的这一情形。收益率的标准差并未将两者加以区分，它仅仅简单地表现为是对二者中值的偏离。只要概率分布或多或少与中值是对称的,σ就可以精确测度风险，特别地，当我们假定概率分布为正态分布（即通常的铃形曲线）时,E(r)与 σ就充分准确地体现了概率分布的特点。
Clearly,what would trouble potential investors in the index fund is the
downside risk of a –16% rate of return,not the upside potential of a 44%
rate of return,The standard deviation of the rate of return does not
distinguish between these two; it treats both simply as deviations from
the mean,As long as the probability distribution is more or less
symmetric about the mean,σis an adequate measure of risk,In the
special case where we can assume that the probability distribution is
normal—represented by the well-known bell-shaped curve—E(r)
andσare perfectly adequate to characterize the distribution.
概率分布特性
Characteristics of Probability Distributions
5-17
对称分布 Symmetric distribution
中值 mean
s.d,s.d.
正态分布
Normal Distribution
5-18
风险和风险溢价
Risk and Risk Premiums
回报分为两种：一种是投资于指数基金的期望总收益，一种是投资于譬如国库券、货币市场工具或银行存款上的无风险收益率。两者之差我们称之为普通股风险溢价。如果例中的无风险收益率每年为 6%，指数基金期望收益率每年为 14%，那么股票的风险溢价每年就为 8%。
We measure the reward as the difference between the
expected HPR on the index stock fund and the risk-free rate,
that is,the rate you can earn by leaving money in risk-free
assets such as T-bills,money market funds,or the bank,We
call this difference the risk premium on common stocks,If
the risk-free rate in the example is 6% per year,and the
expected index fund return is 14%,then the risk premium on
stocks is 8% per year,
5-19
年持有期收益率的概率分布
Annual Holding Period Returns
几何平均 算术平均 标准差
Geom,Arith,Stan.
类列 Series Mean% Mean% Dev.%
大公司股票 Lg,Stk 10.51 12.49 20.30
小公司股票 Sm,Stk 12.19 18.29 39.28
长期国家基金 LT Gov 5.23 5.53 8.18
国库券 T-Bills 3.80 3.85 3.25
通货膨胀率 Inflation 3.06 3.15 4.40
5-20
类别 风险溢价 实际收益
Risk Real
Series Premiums% Returns%
Sm Stk 15.0 15.6
Lg Stk 9.3 9.9
LT Gov 1.6 2.2
T-Bills --- 0.6
Inflation --- ---
年持有期风险溢价和实际收益
Annual Holding Period Risk Premiums
and Real Returns
5-21
经济的真实利率的均衡水平由居民储蓄意愿（影响资金供给曲线）和企业投资 固定资产、厂房设备的期望利润率水平（影响需求曲线）决定。此外也受政府财政政策和货币政策的影响。
The economy’s equilibrium level of real interest
rates depends on the willingness of households to
save,as reflected in the supply curve of funds,
and on the expected profitability of business
investment in plant,equipment,and inventories,
as reflected in the demand curve for funds,It
depends also on government fiscal and monetary
policy,
summary
5-22
名义利率等于真实均衡利率加上通胀率。通常，我们只能直接得到名义利率,我们必须通过通胀预期来推断真实利率。
The nominal rate of interest is the
equilibrium real rate plus the expected rate
of inflation,In general,we can directly
observe only nominal interest rates; from
them,we must infer expected real rates,
using inflation forecasts.
summary
5-23
任何证券的均衡期望收益率均由其均衡真实收益率、期望通胀率和证券特别风险溢价三者相加而成。
The equilibrium expected rate of return on
any security is the sum of the equilibrium
real rate of interest,the expected rate of
inflation,and a security-specific risk premium.
summary
5-24
投资者面临着风险 -期望收益权衡的选择。由本章历史数据的分析得出：低风险资产提供低收益，反之亦然。
Investors face a trade-off between risk and
expected return,Historical data confirm our
intuition that assets with low degrees of risk
provide lower returns on average than do
those of higher risk.
summary
5-25
由于未来通胀率的不确定性，保证获得名义利率的资产实际上存在着风险。
Assets with guaranteed nominal interest
rates are risky in real terms because the
future inflation rate is uncertain.
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