Historical correlations Exhibit 2 正 storical C。e1a心丑sf卫 xcess Returns (anuary I976 trough Azzszst z997) Germany Bonds Curreney Equities Bonds Currency Equities Bonds Currens C 1.00 france 0.o3 ds CH a 1.0 Bandier 0_87 .5 2.DP Currency o.。1 0.21 0.8 Equities CH 0.42 0.20 0.D Bonds CH Currency Bonds cH Equities CH 0.33 .16 0.0 083 0.04 0.yT 0s9.o curency ooo 2了
Historical correlations:
Lnited Kingdom E/noted Stater Canada austraia Equites Curency quities Bonds Equities Bonds Curency Equities Bond LK Equities 100 047 Currency 0.0 0.2 Equit 08023 .m2 100 Bncs 12028 018032 canada 5 quities05502701074018100 bonds 0.18 025 31 82023100 Currency 0.14 0.13 009 024 015032 124 .00 australia Equities 0.50 0.20 015 048 00061 002 0.18 100 017 0.17 02002101801303710 Currency 0.06 0.05 027 07 000019 028 027020
If you use our procedures and calculate and optimal portfolio, with o=10.7%/, you will get portfolio weights of: Optimal Portfolios Based on Historical Average Approach percent of portfolio value) Unconstrained Germany France Japan UK US. Cane dis Australia Currency exp5 78,7 46,5 15.5 286 60 52 Bonds 97 525 4,4 4圣 15 133 440 9.0 with constraints against shorting assets Gerrmany France dapan U五忘 Cannae Australia Currency exposure -160.0 I152 180 28.7 77. 8 13.8 B。ds .6 0.0 888 0.0 0.0 0.0 0.0 0 00 00 00 00 0. Q 00
If you use our procedures and calculate and optimal portfolio, with , you will get portfolio weights of: P =10.7%
We can make a number of points about these optimal portfolios They illustrate what we mean when we claim that standard mean-variance optimization models often generate unreasonable portfolios The use of past excess returns to represent a neutral set of views is equivalent to assuming that the constant portfolio weights that would have performed best historically are in some sense neutral. in reality of course, they are not neutral at all, but rather are a very special set of weights that go short assets that have done poorly and go long assets that have done well in the particular historical period
◼ We can make a number of points about these optimal portfolios. ◼ They illustrate what we mean when we claim that standard mean-variance optimization models often generate unreasonable portfolios. ◼ The use of past excess returns to represent a neutral set of views is equivalent to assuming that the constant portfolio weights that would have performed best historically are in some sense neutral. In reality, of course, they are not neutral at all, but rather are a very special set of weights that go short assets that have done poorly and go long assets that have done well in the particular historical period
a remedy for both of these problems is to use (1)market model to calculate asset covariance, (2)and use the CaPm to determine what market expectation must be, and then combine your "view with the CaPm derived estimates to get portfolio weights. The key input we will need for both of these is the set of asset betas so first we must consider the problem of estimating betas
◼ A remedy for both of these problems is to use ◼ (1) market model to calculate asset covariance, ◼ (2) and use the CAPM to determine what market expectation must be, and then combine your “view” with the CAPM derived estimates to get portfolio weights. ◼ The key input we will need for both of these is the set of asset betas, so, first, we must consider the problem of estimating betas