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Chapter 12: Portfolios without Short Sales

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Classical problem: Unconstrained optimization

 is the Sharpe ratio

Unconstrained: Implementation in Excel

Constrained maximization: No short sales
Constant c is important!

Different c’s will give different porttolios

xi >= 0, I = 1,…,N

Constrained: Implementation in Excel

Start with arbitrary solution
Use Solver, adding two constraints:
Non-negativity
Portfolio sums to 1

Solution with constraints

Changing c changes the portfolio

Short sale constraints negatively impact returns

Excel/Solver can accommodate more complicated constraints

And the answer is …

Variance-covariance matrix Means
0.100.03-0.080.058%
0.030.200.020.039%
-0.080.020.300.2010%
0.050.030.200.9011%
c3.0%<-- This is the constant Optimal portfolio without short sale restrictions (Chapter 9, Proposition 1) 0.6219<-- {=MMULT(MINVERSE(B3:E6),G3:G6-C8)/SUM(MMULT(MINVERSE(B3:E6),G3:G6-C8))} Total 1<-- =SUM(B11:B14) Portfolio mean 8.62%<-- {=MMULT(TRANSPOSE(B11:B14),G3:G6)} Portfolio sigma 19.39%<-- {=SQRT(MMULT(TRANSPOSE(B11:B14),MMULT(B3:E6,B11:B14)))} (mean-constant)/sigma 28.99%<-- =(B17-C8)/B18 PORTFOLIO OPTIMIZATION ALLOWING SHORT SALES Follows Proposition 1, Chapter 9 Variance-covariance matrix Means 0.100.03-0.080.058% 0.030.200.020.039% -0.080.020.300.2010% 0.050.030.200.9011% c5.0%<-- This is the constant Here we start with an arbitrary feasible portfolio and use Solver Total 1<-- =SUM(B11:B14) Portfolio mean 9.02%<-- {=MMULT(TRANSPOSE(B11:B14),G3:G6)} Portfolio sigma 23.81%<-- {=SQRT(MMULT(TRANSPOSE(B11:B14),MMULT(B3:E6,B11:B14)))} (mean-constant)/sigma 16.89%<-- =(B17-C8)/B18 PORTFOLIO OPTIMIZATION WITH MORE COMPLICATED CONSTRAINTS /docProps/thumbnail.jpeg 程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com