The Federal Reserve, ECB, and Bank of England face a tough challenge when it comes to controlling inflation in 2021. This question will ask you to go through different facets of this problem facing a central bank, whose goal is to control inflation at 2%. The central bank sets the long-run nominal interest rate at 2%. In terms of notation / is the nominal interest rate / is the real interest rate * is inflation, and the time period is one year. [22 marks] (a) In the first half of 2020, governments provided large transfers to households and businesses. Given widespread lockdowns, a large share of these funds were deposited in banks, which in turn deposited them at the central bank. Plot in a diagram the market for reserves. Show the effect the policies of 2020 might have on the equilibrium interbank rate if the central bank does nothing in response. Then, show instead, and explain, what happens to the equilibrium in this market in the diagram, and to the equilibrium interest rate, if the central bank in response buys large amount of government bonds and credits the deposit account of banks. [4 marks] (b) In an economy, the arbitrage condition between nominal and real bonds is: i = r+0.02 + where & is random variable with a mean zero (that is an expected value, or long-run value, of zero). What is the long-run value of the real interest rate in this economy? Is this higher than its historical value? Give one reason why it may have changed in the last few years. [3 marks] (c) Before the crisis, the central bank followed this policy rule: i = -0.02+2n Is this rule consistent with the long-run inflation target of 2%? [3 marks] (d) In equilibrium the real interest rate in the economy is given by the expression: r = -0.5(7 - 0.02 - =) so that higher inflation is associated with lower real interest rates. Combine with the previous equations in this question to solve for inflation as a function of the shocks . Intuitively explain whether these shocks are attenuated (have a coefficient less than 1) or are propagated (coeffi- cient larger than 1). [3 marks] (e) In 2021, the central bank promised not to let interest rates rise above 6% no matter what. There- fore the policy rule in question c) now only holds as long as inflation is below 4%; for higher values of inflation, / = 0.06. Solve for inflation as a function of & in this case, that is when i = 0.06. Intuitively explain whether these shocks are attenuated (have a coefficient less than 1) or are propagated (coefficient larger than 1). [3 marks]A company is currently financed entirely by equity with 100,000 shares in issue and no debt. The current share price is $1. The company has total assets of $100,000 with volatility of 15% per annum. The company is considering raising $250,000 by issuing zero-coupon debt with a five- year maturity date. The continuously compounded risk-free rate of interest is 3% per annum. The company intends to set the redemption value of the debt such that the share price will remain unchanged under the Merton model. (i) Give the value of the company's assets immediately after issuing the debt. [1] (ii) Calculate the redemption value of the debt using the Merton model. [5] (iii) Calculate the credit spread on the debt. [2] One year later, the company is struggling. The share price has fallen to $0.50 and the current value of the debt has fallen to $50 per $100 of redemption value. (iv) Calculate the proportionate fall in the value of: (a) the equity. (b) the debt. [2] (v) Suggest why the value of the equity has fallen by proportionately more than the fall in the value of the debt. [3]
