frontier of risky assets   10 Optimal portfolio TD 5   0 0 20 40 60 80 100 Standard deviation (%)         buy orders. With a budget of $220 million, Sigma wants a position in BU of $220,000,000 .8070 $177,540,000, or $177,540,000/39 4,552,308 shares, and a position in TD of $220,000,000 .1930 $42,460,000, which corresponds to 1,088,718 shares.     Sigmas Demand for Shares   The expected rates of return that Sigma used to derive its demand for shares of BU and TD were computed from the forecast of year-end stock prices and the current prices. If, say, a share of BU could be purchased at a lower price, Sigmas forecast of the rate of return on BU would be higher. Conversely, if BU shares were selling at a higher price, expected re- turns would be lower. A new expected return would result in a different optimal portfolio and a different demand for shares. We can think of Sigmas demand schedule for a stock as the number of shares Sigma would want to hold at different share prices. In our simplified world, producing the demand for BU shares is not difficult. First, we revise Table 9.2 to recompute the expected return on BU at different current prices given the forecasted year-end price. Then, for each price and associated expected return, we construct the optimal portfolio and find the implied po- sition in BU. A few samples of these calculations are shown in Table 9.3. The first four columns in Table 9.3 show the expected returns on BU shares given their current price. The optimal proportion (column 5) is calculated using these expected returns. Finally, Sigmas investment budget, the optimal proportion in BU and the current price of a BU share de- termine the