To see how taxes affect after-tax risk in a portfolio context, consider an investor
with 50 percent of her wealth invested in equities and 50 percent invested in fixed
income, both held in taxable accounts. The equity has a pretax standard deviation
of 20 percent and is relatively tax-efficient such that all returns are taxed each
year at a 20 percent tax rate. The fixed income is also taxed annually but at a 40
percent rate with pretax volatility of 5 percent. If the two asset classes are perfectly
correlated, the pretax portfolio volatility is 0.50(0.20) + 0.50(0.05) = 0.125 = 12.5
percent. On an after-tax basis, however, portfolio volatility is 0.50(0.20)(1 − 0.20)
+ 0.50(0.05)(1 − 0.40) = 0.095 = 9.5 percent. This example illustrates that annually
paid taxes reduce portfolio volatility.15
这个perfectly correlated 是不是相关系数为1？那么组合波动是不是该=0.5*0.2+0.5*0.05+2*0.5*0.5*1*0.2*0.05？
教材那个公式是不是应该相关系数=0？
组合波动是这么算吗
