Lending and borrowing

Model separate lending and borrowing assets with different rates and weight constraints.

5 assets. Adapted from Professor Robert Stambaugh’s Finance 205/720 materials. Original example.

Adjust the assumptions and bounds below to find the portfolio that maximizes expected return minus the variance penalty. Calculations remain within the Wharton Backtester application.

Enter numerical values in decimal form: for example, enter a 4% mean return as .04, not 4.0. Initial weights must sum to 1.

Objective Function

E(R) - 0.5 × × Var(R)

Enter the coefficient of risk aversion.

Compute

A two-asset rebalancing to improve the objective

The portfolio that maximizes the objective

Initial Portfolio Parameters

Asset	Mean	St Dev	Initial Weight	Lower Bound	Upper Bound
1 Asset 1
2 Asset 2
3 Asset 3
4 Asset 4
5 Asset 5

Blank bounds are unlimited.

Correlation Matrix

Asset	1	2	3	4	5
1 Asset 1	1.00000
2 Asset 2		1.00000
3 Asset 3			1.00000
4 Asset 4				1.00000
5 Asset 5					1.00000

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