A firm goes to the markets to raise capital. The investor can either invest V₁ on the firm or buy government bonds. If she invests, the expected value of the dividend she receives the following period is Et[Dt+1]. Where Et[] denotes the mathematical expectation, taken at time, t. If she buys a government bond, and receive a gross return (1 + r) for sure. 1. Let Et [Vt+1] denote the expected value of the stock the following period, explain why this is not the only return that the investor can expect from owning the stock. 2. Write down an expression for the gross return on the stock. [Hint: This is a ratio.] 3. Suppose investor's objective is to maximize their expected return. If the return from bonds is higher than the expected return from stocks, will they buy stocks or bonds? How about the other way around? 4. Since investors hold both stocks and bonds, what must be true about the expected return of stocks and bonds in equilibrium? Show that this implies the following no arbitrage condition: V₁ = E[D+1+Vi+1] 1 + rt (29.1) 5. If equation (29.1) describes the stock market, what three variables determine its value? 6. Let ut = log Vt. Show that the equilibrium growth rate of the stock market is given by the following relationship: v-v-1 = -(rt-rt-1) + (log(Et[Dt+1+Vt+1]) - log(Et-1 [Dt + V) (29.2)

A firm goes to the markets to raise capital. The investor can either invest V₁ on the firm or buy government bonds. If she invests, the expected value of the dividend she receives the following period is Et[Dt+1]. Where Et[] denotes the mathematical expectation, taken at time, t. If she buys a government bond, and receive a gross return (1 + r) for sure. 1. Let Et [Vt+1] denote the expected value of the stock the following period, explain why this is not the only return that the investor can expect from owning the stock. 2. Write down an expression for the gross return on the stock. [Hint: This is a ratio.] 3. Suppose investor's objective is to maximize their expected return. If the return from bonds is higher than the expected return from stocks, will they buy stocks or bonds? How about the other way around? 4. Since investors hold both stocks and bonds, what must be true about the expected return of stocks and bonds in equilibrium? Show that this implies the following no arbitrage condition: V₁ = E[D+1+Vi+1] 1 + rt (29.1) 5. If equation (29.1) describes the stock market, what three variables determine its value? 6. Let ut = log Vt. Show that the equilibrium growth rate of the stock market is given by the following relationship: v-v-1 = -(rt-rt-1) + (log(Et[Dt+1+Vt+1]) - log(Et-1 [Dt + V) (29.2)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.9P

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