WACC 1

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The task of choosing the optimal portfolio is a lengthy one but entails some very well defined steps and formulas. The first
part of the report deals with formulation of the optimal portfolio consisting of stocks listed with the Dow 30 index, while
the last part would deal with utility scores and the client’s risk appetite.
I would systematically present formulas and explain every part of portfolio construction as the report proceeds.
The first in the series of steps is annualizing monthly stock returns by multiplying each value by 12. Excess returns are
then calculated by subtracting the T-bill rate (Exhibit 1) from these annualized stock returns.

Exhibit 2a!B5 is the monthly stock return
Exhibit 1!C68 is the T-bill rate for year 1990.
Averages of these annualized excess returns are then calculated as a naïve forecast for expected returns.

Bordered Covariance Matrix is next in this series of steps. The covariance matrix is made using the ‘covariance’ option in
Excel’s Data Analysis tool by selecting the entire excess return data sheet.

The actual portfolio construction process starts with the determination of risk return opportunities available to the investor.
All such opportunities are summarized and graphically represented by the minimum-variance frontier of risky assets.
Formulas used to find portfolio expected return, portfolio standard deviation and the Sharpe ratio are listed below. In
addition, Solver was used to determine weights and the portfolio combination with the least amount of variance for a given
portfolio expected return.
Portfolio expected return= sumproduct(all weights, expected returns)

Since portfolio standard deviation, like the expected return, is the weighted average of individual standard deviations I first
calculated standard deviations for each stock using the formula
Stock risk = stock’s weight * sumproduct( all weights, stock’s covariance with all other stocks) as shown in the picture
below

Portfolio standard deviation = sum (all stdev of individual stocks) ^ 0.5 was then used to calculate the portfolio’s variance.
The slope or the Sharpe ratio was calculated by simply dividing the portfolio expected return by portfolio standard
deviation.
To find the minimum variance portfolio, standard deviation was set as the objective function to be minimized by solver.
The resulting mean, standard deviation, slope and weights were copied and pasted on a table to chart out the efficient
frontier. Next we used the solver ad on to locate the optimum risky point on this frontier i.e. the portfolio with the highest
reward to volatility ratio. For this we selected the slope as our objective function and requested the solver to maximize it.
The mean, SD, slope and weights that ensured gave me a fair idea as to help me plot other points. I then changed expected
return values within the range and asked solver to maximize the slope. All values and their weights were copied and pasted
in the table made earlier for construction of the efficient frontier. I in fact mad e to tables, one for short sales and one in
which short sales was not allowed.

Weights
The CAL or the Capital Allocation Line is the one that is tangent to the optimum risky portfolio, this line has the highest
Sharpe ratio or in other words the greatest reward to variability ratio. The determination of CAL effectively marks the end
of work for the investment manager since allocation of the complete portfolio of T-bills versus the risky portfolio depends
on the degree of risk aversion of the client.
As can be seen in the picture above, the CAL line was constructed by multiplying each security’s standard deviation with
the slope of the optimum risky portfolio. Two different CAL lines were plotted each for short sales and with no short sales.
Below is the graph for short sales.

Weights

Picture of the table used to plot the CAL line under no short sales criteria is also given below.

The CAL line under this situation is graphed below

ANALYSIS

The following table supplements our financial belief that the higher the risk the higher the return. The other insight that we
get is that short selling is a much better strategy than going without short selling. T he optimum portfolio gives a much
better incremental return to incremental risk than when the manager decides not to sell borrowed security.
What is amazing though is the higher Sharpe ratio of the Index Return but with lower volatility and lower expected return
than our selected portfolio. One reason for this could be that Index returns are better diversified and have a broader
selection of asset classes giving them the cushion and the advantage over actively managed funds.

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