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f your risk-aversion coefficient is A = 4 and you believe that the entire 1926–2015 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is U = E(r) – 0.5 × Aσ2. and 51.05%

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Answer:

The portfolio should invest 48.94% in equity while 51.05% in the T-bills.

Explanation:

As the complete question is not given here ,the table of data is missing which is as attached herewith.

From the maximized equation of the utility function it is evident that

[tex]Weight=\frac{E_M-r_f}{A\sigma_M^2}[/tex]

For the equity, here as

  • [tex]Weight[/tex] is percentage of the equity which is to be calculated
  • [tex]{E_M-r_f}[/tex] is the Risk premium whose value as seen from the attached data for the period 1926-2015 is 8.30%
  • [tex]A[/tex] is the risk aversion factor which is given as 4.
  • [tex]\sigma_M[/tex] is the standard deviation of the portfolio which from the data for the period 1926-2015 is 20.59

By substituting values.

[tex]Weight=\frac{E_M-r_f}{A\sigma_M^2}\\Weight=\frac{8.30\%}{4(20.59\%)^2}\\Weight=0.4894 =48.94\%[/tex]

So the weight of equity is 48.94%.

Now the weight of T bills is given as

[tex]Weight_{T-Bills}=1-Weight_{equity}\\Weight_{T-Bills}=1-0.4894\\Weight_{T-Bills}=0.5105=51.05\%\\[/tex]

So  the weight of T-bills is 51.05%.

The portfolio should invest 48.94% in equity while 51.05% in the T-bills.

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