国际多元化投资组合 (英文版)International Portfolio Diversification

Key results of portfolio theory
The extent to which risk is reduced by portfolio diversification depends on the correlation of assets in the portfolio.
Foreign bonds U.S. bonds
“Asset Allocation.” Jorion, Journal of Portfolio Management, Summer 1989.
20-16
Return on a foreign asset
Recall Ptd = PtfStd/f (Ptd/Pt-1d) = (1+rd)
20-6
Key results of portfolio theory
The extent to which risk is reduced by portfolio diversification depends on the correlation of assets in the portfolio.
Diversification 20.4 Variances on Foreign Stock and Bond
Investments 20.5 Home Bias 20.6 Summary
20-1
Perfect financial markets ...a starting point
Frictionless markets
- no government intervention or taxes - no transaction costs or other market frictions
Rational investors with equal access to costless information and market prices
20-3
Expected return on a portfolio
E[ri]
si
A American J Japanese
11.8% 17.8% 15.4% 36.5%
Example: Equal weights of A and J
E[rP] = xA E[rA] + xJ E[rJ] = (½)(0.118)+(½)(0.154)
Can Fra Ger Jap Swi UK US
France 0.472
Germany 0.388 0.645
Japan 0.320 0.399 0.364
Swiss
0.464 0.618 0.670 0.430
U.K.
0.513 0.559 0.451 0.369 0.569
U.S.
0.727 0.482 0.443 0.304 0.504 0.522
Chapter 20
International Portfolio Diversification
20.1 The Algebra of Portfolio Diversification 20.2 Mean-Variance Efficiency 20.3 The Benefits of International Portfolio
sP = (0.0511)1/2 = 0.226, or 22.6%
20-5
Key results of portfolio theory
The extent to which risk is reduced by portfolio diversification depends on the correlation of assets in the portfolio.
Austria Italy
New Zealand Portugal
Greece Singapore Norway
20-13
International stock returns
(Dollar returns to US investors from 1970-2002)
Canada France Germany Japan Switzerland U.K. U.S. World
Expected return
W M
rF
Standard deviation of return
- Potential for higher returns - Potential for lower portfolio risk
20-11
Domestic versus international diversification
Var(r$) 1.000 1.000 1.000 1.000 1.000 1.000
- All investors rationally price financial securities - All investors have equal access to costless
information - All investors have equal access to market prices
xi = proportion of wealth in asset i, s.t. Si xi = 1
Expected return on a portfolio E[rP] = Si xi E[ri]
Portfolio variance Var(rP) = sP2 = Si Sj xi xj sij where sij = rij si sj
20-8
Diversification
Mean annual return
16%
J
r=-
14%
1
r=
r=
+0.304
+1
12%
A
10% 0%
10%
20%
30%
Standard deviation of annual return
40% 20-9
Mean-variance efficiency
Mean annual return
Interaction + Var(s$/f) + terms = + 0.033 + 0.053 = + 0.149 + -0.086 = + 0.194 + -0.167 = + 0.182 + 0.005 = + 0.298 + -0.225 = + 0.127 + -0.029 =
0.911 + 0.164 + -0.075 =
bW versus the MSCI world stock market index Sharpe Index (SI) = (rP - rF) / sP
20-14
International equity correlations
(Dollar returns to US investors from 1970-2002)
Mean 10.4 14.0 12.5 15.4 14.2 14.6 11.8 0.112
Stdev 18.8 29.1 30.0 36.5 25.5 29.4 17.8 0.176
bW 0.79 1.09 1.05 1.39 0.98 1.14 0.87 1.00
SI 0.17 0.23 0.18 0.23 0.28 0.25 0.26 0.23
20-2
The algebra of portfolio theory
Assumptions
- Nominal returns are normally distributed - Investors want more return and less risk in
their functional currency
Portfolio risk relative to
the risk of a single asset
(sP²/si²)
U.S. diversification only
1.0
International diversification
0.5
5
10
15
20
25
Number of stocks in portfolio
30%
Investment opportunity set
20% 10%
Efficient frontier
A
J B
0% 0%
10%
20%
30%
Standard deviation of annual return
40% 20-10
The promise of international portfolio diversification
26% 12%
20-12
Historical stock market performance
(1970-2002)
Hong Kong
Finland
Sweden Belgium Denmark Japan
Netherlands Swiss US
UK
France Germany
Spain
Australia Canada Ireland World
and (Std/f/St-1d/f) = (1+sd/f)
Return on a foreign asset
(1+rd) = (Ptd/Pt-1d) = (PtfStd/f/Pt-1fSt1d/f) = (Ptf/Pt-1f)(Std/f/St-1d/f) = (1+rf)(1+sd/f)
= 1+rf+sd/f+rfsd/f
(20.7)
20-17
Return statistics on foreign assets
Expected return
E[rd] = E[rf]+E[sd/f]+E[rfsd/f]
Var(rd)
= Var(rf )+Var(sd/f )+Var(rfsd/f ) +2Cov(rf,sd/f)+2Cov(rf,rfsd/f)+2Cov(sd/f,rfsd/f) =Var(rf) + Var(sd/f) + (interaction terms)
20-18
Variance of return on foreign stocks
(from the perspective ofபைடு நூலகம்a US investor)
Canada France Germany Japan Switzerland U.K.
Average
Var(rf) 0.915 0.937 0.973 0.813 0.928 0.902
World 0.735 0.657 0.618 0.671 0.674 0.685 0.855
20-15
International asset allocation
Internationally diversified stocks and bonds
Foreign stocks
U.S. stocks and bonds U.S. stocks
= 0.136, or 13.6%
20-4
Variance of a portfolio
E[ri]
si
A American 11.8% 17.8%
J Japanese 15.4% 36.5%
Correlation
A
J
1.000 0.304
0.304 1.000
sP2 = xA2 sA2 + xJ2 sJ2 + 2 xA xJ rAJ sA sJ = (½)2(0.178)2 + (½)2(0.365)2 + 2(½)(½)(0.304)(0.178)(0.365) = 0.0511
As the number of assets increases, portfolio variance becomes more dependent on the covariances (or correlations) and less dependent on variances.
20-7
As the number of assets increases, portfolio variance becomes more dependent on the covariances (or correlations) and less dependent on variances.
The risk of an asset when held in a large portfolio depends on its covariance (or correlation) with other assets in the portfolio.