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$300,000, of which $90,000 is invested in the Ready Asset money market fund, a risk-free asset for prac- tical purposes. The remaining


$210,000 is invested in risky securities-$113,400 in equi- ties (E) and $96,600 in long-term bonds (B). The equities and long bond holdings comprise "the" risky portfolio, 54% in E and 46% in B:   113,400 E: w1 210,000 .54   B: w 96,600 .46 2 210,000   The weight of the risky portfolio, P, in the complete portfolio, including risk-free and risky investments, is denoted by y:   210,000 300,000 .7 (risky assets) 90,000 300,000 .3 (risk-free assets)   The weights of each stock in the complete portfolio are as follows:   $113,400 $300,000 .378 $96,600 $300,000 .322 Risky portfolio .700   The risky portfolio is 70% of the complete portfolio. Suppose that the owner of this portfolio wishes to decrease risk by reducing the allo- cation to the risky portfolio from y .7 to y .56. The risky portfolio would then total only .56 $300,000 $168,000, requiring the sale of $42,000 of the original $210,000 of risky holdings, with the proceeds used to purchase more shares in Ready Asset (the money market fund). Total holdings in the risk-free asset will increase to $300,000 (1 .56) $132,000, or the original holdings plus the new contribution to the money market fund:   $90,000 $42,000 $132,000   The key point, however, is that we leave the proportions of each asset in the risky port- folio unchanged. Because the weights of E and B in the risky portfolio are .54 and .46, respectively, we sell .54 $42,000 $22,680 of E and .46 $42,000 $19,320 of B. After the sale, the proportions of each asset in the risky portfolio are in fact unchanged:   113,400 22,680 E: w1 210,000 42,000 .54 96,600 19,320 B: w2 210,000 42,000 .46 II. Portfolio Theory 7. Capital Allocation between the Risky Asset and the Risk−Free Asset The McGraw−Hill