# Question

Assume that the investor’s tax rate is 40% and that in a competitive equilibrium all assets must earn the same after tax after risk adjusted returns of 7% (= r*) for the investor to be indifferent between the assets. The investor is considering two assets: asset 1 and asset 2. The required pretax total rate of return Ro on asset 1 is 16% and on asset 2 is 14%. Analyze the following three cases.

Case 1. Suppose both assets are fully taxable— that is, g = 1. Because both assets are fully taxable, it is obvious that they must be of different risk for the required pretax total rates of return to differ. What is the pretax risk premium, Rrp, for each asset? From a purely tax standpoint, which asset will the marginal investor prefer?

Case 2. Suppose both assets are equally risky with a required after tax risk premium of Rrp = 3.5%. Because both assets are equally risky, it is obvious that they must be differentially taxed for the required pretax total rate of return to differ. Suppose g1 = .86 and g2 = .625, where g is the percentage of income from the asset included in taxable income and the subscript denotes asset 1 and 2, respectively.

Show that the investor will be indifferent between the two assets (from a tax standpoint).

Which asset would you choose if your marginal tax rate was 30%?

Which asset would you choose if your marginal tax rate was 50%?

Case 3. Now suppose both assets are differentially taxed and differentially risky. For asset 1, g1 = .80 and Rrp = 3.88%. For asset 2, g2 = .20 and Rrp = 5.88%. (Because the after tax risk premiums differ between the two assets, they are not equally risky.)

Which asset is tax favored? Which asset is more risky?

Which asset will the investor (with a marginal tax rate of 40%) prefer?

Which asset would you choose if your marginal tax rate was 30%?

Which asset would you choose if your marginal tax rate was 50%?

Case 1. Suppose both assets are fully taxable— that is, g = 1. Because both assets are fully taxable, it is obvious that they must be of different risk for the required pretax total rates of return to differ. What is the pretax risk premium, Rrp, for each asset? From a purely tax standpoint, which asset will the marginal investor prefer?

Case 2. Suppose both assets are equally risky with a required after tax risk premium of Rrp = 3.5%. Because both assets are equally risky, it is obvious that they must be differentially taxed for the required pretax total rate of return to differ. Suppose g1 = .86 and g2 = .625, where g is the percentage of income from the asset included in taxable income and the subscript denotes asset 1 and 2, respectively.

Show that the investor will be indifferent between the two assets (from a tax standpoint).

Which asset would you choose if your marginal tax rate was 30%?

Which asset would you choose if your marginal tax rate was 50%?

Case 3. Now suppose both assets are differentially taxed and differentially risky. For asset 1, g1 = .80 and Rrp = 3.88%. For asset 2, g2 = .20 and Rrp = 5.88%. (Because the after tax risk premiums differ between the two assets, they are not equally risky.)

Which asset is tax favored? Which asset is more risky?

Which asset will the investor (with a marginal tax rate of 40%) prefer?

Which asset would you choose if your marginal tax rate was 30%?

Which asset would you choose if your marginal tax rate was 50%?

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