Final Week Assignment This is a tutorial-length set of examination-style questions on topics arising in the unit. Present answers as you would in an examination. Give emphasis to diagrams where they are relevant, do not write long and dense paragraphs and keep the answers relevant by drawing on material covered in the lectures, tutorials or the references. Hand writing is fine – practice keeping it easy to read (and draw diagrams large and in pencil). Word processed answers are also acceptable, though bear in mind that this is not possible in an examination. Try to keep answers to no more than the equivalent of one hand-written page each. No answers or answer guides will be available but the questions will be discussed during the final tutorial of the semester. Due by 11am, Monday 22 October. Q1: A ten-year Treasury bond issued on 1 January 2008 has face value $100,000 and annual coupon $7,000, paid on 1 January of every subsequent year. Recall that, if the duration is D, the yield is RY and the coupon payments associated with it are Ct (the final of which includes the principal), the bond’s price and duration are: and its price and yield are related by: a) Calculate the duration of this bond as of 2 January 2012 and its trading price if the market yield at that duration is 5.0%/yr. b) If the yield were to rise by 250 basis points, by what proportion would the bond price change? Calculate this using the marginal expression and by using the price formula, noting and explaining any differences. Would this change have been larger had the bond had initial maturity 20 years? Briefly explain why. Q2: Define rC as the certainty equivalent rate of return, rM as the rate of return from the market portfolio and rS as the risk free rate of return. We can translate our portfolio manager’s objective function on $ returns into rates of return as the maximisation of rC with a risk premium (measured as the equivalent sacrifice in the rate of return due to risk) of RsP 2 /2, where sP is the standard deviation of the portfolio rate of return (or the coefficient of variation of its $ returns). 1 1 ? ? ? ? 1 , 1 1 n n t t t t t t Y Y C C B Dt ? ? R R B ?? ?? ? ? ?? ?? ? ? ?? ?? ? ? ? ? 1 Y Y Y dB D dR DdR B R ?? ?? ? ? ? 2 1 2 CP P R rr s ? ? (a) If the market portfolio yields rM= XXXXXXXXXX%) with standard deviation sM=0.15 and the risk free asset yields rS=0.06 (6%) formulate the mean and standard deviation of the portfolio rate of return in terms of the share of the risk-free asset, ?, rM , rS and sM. (b) Eliminate ? to obtain an expression for the linear part of the efficient frontier. Then sketch the frontier, the manager’s indifference curves and the chosen optimal portfolio. (c) Calculate the optimal portfolio return and risk and the optimal share of the risk free asset for the case in which the manager has R=4. (d) Recalculate the optimum share of the risk free asset when an external shock raises the riskiness of the market portfolio to sM=0.40. Show this new result on your sketch and briefly discuss the economic implications of such a shock. Q3: A small open economy runs a current account deficit and it is subjected to an increase in the riskiness of home assets that induces a rise in the share of home money in portfolios and therefore raises the cash to deposit ratio of households and the reserve to deposit ratio of financial institutions. Think of the central bank as being in a “liquidity trap” situation, so that the monetary base, MB, is forced to remain constant (the central bank cannot lower the short rate so cannot induce the holding of additional base money). Alternatively, the central bank recognizes that it is “pushing on a piece of string” any change in MB would only induce further holding of money by financial institutions and households and so not raise MS. a) Initially, assume its labour market clears, retaining full employment. Use diagrams to illustrate the effects of this shock on the current account, the interest rate the real exchange rate, the nominal money supply and the nominal exchange rate. Briefly explain your results. b) Noting the direction of the change in the price level, explain the effects on employment and GDP if the nominal wage is fixed. c) Given that the monetary base is fixed and hence the central bank has no control over the nominal money supply, MS, the government resorts to fiscal policy. Use your diagrams to help discuss the corresponding effects of a responding fiscal expansion, G?, that is large enough to induce an inflation. Q4: An economy in a liquidity trap runs a current account deficit and faces unemployment. Its central bank wishes to create an inflation so as to induce firms to rehire their workers. A sufficient rise in the monetary base can only be achieved via “quantitative easing” (QE). Assume the money multiplier is low but cannot decrease further (the money shares of private and financial institutional portfolios are as high as risk averse agents want them). a) Briefly explain the nature of a liquidity trap and what is meant by “quantitative easing”. b) Make the initial assumption of a clearing labour market and then use diagrams to determine the sign of changes to the home long term bond yield, the level of private investment, the current account balance, the real exchange rate, the price level and the nominal exchange rate.1 If the shock is large enough to induce an inflation, suggest the consequence in the home labour market if there is nominal wage rigidity. c) Imagine the country is the US. Briefly discuss the implications of this US policy for other countries and, in particular, how it would affect their price levels and exchange rates. d) Explain how your analysis in b), above, changes if investors expect an inflation? Would the QE shock need to be bigger or smaller? Briefly discuss the possible outcomes if they expect both increased inflation and a real depreciation?