Question #64230

Assume that risk neutral investors decide whether to invest in a risk-free bond with interest rate i0 or a government bond with default risk. With probability ω investors lose their investment in the government bond (including the interest payment). With probability 1 − ω investors receive interest rate i. Mark the correct statements.

In addition, suppose that the default risk of the government bond is increasing in the interest rate as follows: ω = ω0 + βi.

5. Assume that ω0 = 0, β = 1 and i0 = 0. Mark the correct statements.

(a) There are multiple equilibrium interest rates i for government-bonds. (b) There are exactly two equilibrium interest rates i.

(c) There is a unique equilibrium interest rate i = 0%.

(d) There is a unique equilibrium interest rate i = 100%.

(e) There are two equilibria: i = 0 % and i = 100 %.

I get 0% but others think also 100% is correct,, but if you set in the equation .. 100% isnt possible.. Or could someone help me with formula?

In addition, suppose that the default risk of the government bond is increasing in the interest rate as follows: ω = ω0 + βi.

5. Assume that ω0 = 0, β = 1 and i0 = 0. Mark the correct statements.

(a) There are multiple equilibrium interest rates i for government-bonds. (b) There are exactly two equilibrium interest rates i.

(c) There is a unique equilibrium interest rate i = 0%.

(d) There is a unique equilibrium interest rate i = 100%.

(e) There are two equilibria: i = 0 % and i = 100 %.

I get 0% but others think also 100% is correct,, but if you set in the equation .. 100% isnt possible.. Or could someone help me with formula?

Expert's answer

5. If ω0 = 0, β = 1 and i0 = 0, then ω = 0 + 1 = 1 and risk neutral investors will invest in a risk-free bond with interest rate i = 0% or i = 100%, so the correct statement is:

(e) There are two equilibria: i = 0 % and i = 100 %.

(e) There are two equilibria: i = 0 % and i = 100 %.

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