FIN 30220: Macroeconomic Analysis

1. FIN 30220: Macroeconomic Analysis Capital Markets

2. Recall that production is a function of labor, capital and technology. Capital Markets determine investment, which affects the evolution of the capital stock over time Annual Depreciation Rate Purchases of New Capital Tomorrow’s capital stock Remaining portion of current capital stock

3. t = 0 The US Economy t = 1 Output/Income Determined Capital Stock = Capital Stock = Productivity = Productivity = The labor market in t=1 begins Production is allocated to various uses Labor Markets Determine employment New capital is added to existing stock

4. 2010 The US Economy 2011 GDP = $14,500B Private Nonresidential Fixed Assets $17,346B Private Nonresidential Fixed Assets $16,946B Total Employment 132M Total Employment 130M

5. How was our net investment of $400B financed? Gross Domestic Product = $14,500B Net Factor Payments ($200B) Gross National Product = $14,700B Depreciation/Indirect Taxes ($2,200) 130M National Income = $12,500B We used 130M people and $16.9T worth of private capital to produce $14.5T in output!!

6. Financial Markets allocate saving to finance borrowing Saving Households: $500B Business: $800B $1,800B Government Deficit $1,400 B Financial Markets Current Account -$500B Net Investment $400B

7. Financial Markets Commercial Banks accept deposits from one group (savers) and lends those funds out to others (borrowers) Investment Banks buy bonds from one group (borrowers) and sell those bonds to others (savers) Bond Price Real interest rate

8. Financial Markets Suppose that government runs a large deficit. The increase in the demand for loanable funds should rise...this increases the interest rate The government borrows money by selling bonds. The increased supply of bonds should lower bond prices

9. Alexander Hamilton was appointed by George Washington as the first Secretary of the Treasury in 1789. The US government has had outstanding debt securities in global financial markets ever since. As of February 2015, total debt of the US government was equal to $18,141,000,000,000.00 $13,038,000,000,000.00 $5,103,000,000,000.00 Debt held by the public (net debt) measures outstanding government securities in financial markets Intergovernmental Debt (one branch of government borrowing from another – not “real” debt)

10. US Government Securities can be broadly categorized marketable and non-marketable Non Marketable Debt includes all Treasuries securities that can’t be traded after initial purchase Marketable Debt includes all Treasuries that can be resold after their initial purchase. Virtually all US debt is in marketable securities • Savings Bonds • State and Local Government Series (Slugs) • Rural Electrification Administration series • Bills (< 1 year maturity) • Notes (1- 10 year maturity) • Bonds ( > 10 year maturity) • Inflation Indexed Notes/Bonds

11. Treasury Bills make one payment of principal upon maturity. Consider a 90 Day T-Bill with a face value of $1,000 selling for $997 today 90 days Pay $997 Receive $1,000 What is your (annualized) return on the bond? Bond Equivalent Yield Discount Yield

12. We could do the same calculation in reverse. Consider a 90 Day T-Bill with a face value of $1,000 today 90 days Pay Price P Today Receive $1,000 Suppose you required a 2% annualized return (Bond Equivalent Yield) . What would you be willing to pay? ( 995 4/32)

13. We could do the same calculation in reverse. Consider a 90 Day T-Bill with a face value of $1,000 today 90 days Pay Price P Today Receive $1,000 Suppose you required a 2% annualized return (Discount yield). What would you be willing to pay?

14. Bond Prices vs. Bond Yields today 90 days Pay Price P Today Receive $1,000 Note that there is a negative relationship between prices and yields As yields go up, prices go down! or

15. Interest Rates tend to rise during expansions and fall during recessions 90 Day T-Bill: Secondary Market Price Yield Recession Recession

16. A yield curve represents the average annual returns for securities of different maturities. Now 1 Year 2 Years 3 Years 4 years Average annual return on a 4 year bond purchased today Average annual return on a 3 year bond purchased today Average annual return on a 2 year bond purchased today Average annual return on a 1 year bond purchased today These interest rates are referred to as “spot interest rates”.

17. Suppose we observe a current set of spot rates 2.5% 2 % Now 1 year 2 years 3 years 4 years Consider two investment strategies Strategy #1: Invest $1 in a 2 year Bond. Your 2 year cumulative return is Strategy #2: Invest $1 in a 1 year bond and then reinvest in a one year bond in one year. Your 2 year cumulative return is For these strategies, to pay the same return:

18. Forward rates are not observed, but can be calculated given any two spot rates 2.5% 2% Now 1 year 2 years 3 years 4 years 3% Return on a 1 year security Purchase date is 1 year from today

19. Given any yield curve, we can calculate an expected path for forward rates: Now 1 Year 2 Years 3 Years 4 years

20. Alternatively, suppose we know the path of forward rates… 2% 2.5% Now 1 Year 2 Years 3 Years 4 years Again, consider two investment strategies Strategy #2: Invest $1 in a 2 year Bond. Your 2 year cumulative return is Strategy #1: Invest $1 in a 1 year bond and then reinvest in a one year bond in one year. Your 2 year cumulative return is For these strategies, to pay the same return:

21. Given a set of forward rates, we can calculate the implied spot rates 4 years Now 1 Year 2 Years 3 Years 2% 2.5% 3% 3.5% Spot rates are based on the geometric average of expected future rates

22. What can we learn from the US yield curve?

23. Suppose that expected future rates were expected to be constant 4 years Now 1 Year 2 Years 3 Years 3% 3% The yield curve is flat! 3% 3%

24. An upward sloping yield curve suggests that the market expects interest rates to rise in the future…with one small problem.. Strategy #1: Invest $1 in a 2 year Bond. Your 2 year cumulative return is Strategy #2: Invest $1 in a 1 year bond and then reinvest in a one year bond in one year. Your 2 year cumulative return is For these strategies, to pay the same return.. Are these two strategies actually equivalent?? Strategy #1 is less flexible and, hence, a bit riskier! Therefore, the 180 day rate has two components: and expected future rate AND a liquidity premium

25. Finally, any security with “default risk” will offer a higher rate of return to compensate investors for the possibility of default. Large Spread Small Spreads

26. Suppose that you invest $945 in a one year, $1,000 T-Bill. Prices are listed below as well Now 1 Year Receive $1,000 CPI = 104 Pay $945 CPI = 100 Now, lets convert your $1,000 to current prices and redo the yield This is your inflation adjusted, or, real return

27. Recall that nominal (currency) variables are meaningless without some mention of prices. The same hold for interest rates. Now 1 Year Receive $1,000 CPI = 104 Pay $945 CPI = 100 Inflation Rate = 4% Exact Method Approximation

28. US Real Returns (1948-2014)

29. At the time you bought the asset, you did not know what inflation would be. Now 1 Year Receive $1,000 Pay $945 CPI = 100 Your Expectation: CPI = 102 Actual: CPI = 104 Expected inflation Ex Ante Actual inflation Ex Post We can only measure ex post real interest rates!!

30. Every interest rate can be broken up into (at least) three components Interest Rate Liquidity Premium Risk Premium Inflation Premium = “Base” Rate + + + We will explain this rate These are explained elsewhere

31. Households and Capital Markets From the household’s perspective, capital markets provide an important service. They allow households to reallocate their wealth across time. Note that wealth is not the same as income. Suppose that you earn $50,000 per year (income). You expect to work for 40 years. Your wealth is defined as the present value if your lifetime income. Suppose that the interest rate is 4% (i = .04).

32. Saving and Consumption Without capital markets, consumption equals income at every point in time $50,000 Savings < 0 (Borrowing) With capital markets, total lifetime consumption equals total lifetime wealth $50,000 Savings > 0

33. Generally, it’s your income that fluctuates over time. Your goal is to use capital markets to maintain a constant stream of consumption Peak earning power occurs just prior to retirement S > 0 S < 0 S < 0 $0 Young (0 – 30) Middle Age (30 – 60) Old (60 - ? )

34. Consider the following example. You currently are earning $80,000, but expect to earn $20,000 next year. You can borrow and lend at 5% interest. Further, assume that P = 1 and there is no inflation. Today, you can either save (S>0) or borrow (S<0) Current saving influences future consumption PV of Lifetime Consumption Wealth

35. Future Consumption All your wealth spent next year Consumption equals income 104,000 S > 0 All your wealth spent this year S < 0 20,000 Slope = 1.05 Current Consumption 80,000 99,047

36. What you choose to do depends on your preferences! Total Utility (Happiness) Current Consumption Future Consumption Value of current consumption The consumption that dollar could’ve purchased? What’s that lost consumption worth to you? Save $1 today, what does it cost you? Value of future consumption The dollar saved plus the interest? What’s that extra consumption worth to you? Save $1 today, what do you gain next year? Real return on savings

37. Recall that maximizing anything requires equating costs and benefits at the margin Benefits of saving Cost of saving = Let’s rewrite this… Marginal Rate of substitution measures the value of current consumption in terms of future consumption Marginal Rate of Substitution

38. Future Consumption Real Interest Rate 104,000 51,500 20,000 50,000 80,000 99,047 Savings Savings = 30,000 Current Consumption

39. Suppose that the interest rate increases to 8%... Substitution effect: As interest rates rise, current consumption becomes more expensive –spend less today! (Save More) Real Interest Rate Income Effect Substitution effect Income Effect: As interest rates rise, you earn more interest income –spend more today! (Save Less) 104,000 51,500 20,000 50,000 80,000 99,047 Savings 40,000 60,000 Current Consumption

40. We typically assume that the substitution effect is dominant…a rise in the real interest rate increases savings. Real Interest Rate 104,000 62,000 20,000 40,000 80,000 99,047 Savings Savings = 40,000

41. Suppose that your current income increases to $100,000… Future Consumption Real Interest Rate 104,000 62,000 51,500 20,000 50,000 60,000 100,000 Savings Savings = 40,000 A rise in current income increases savings

42. Suppose that your current income stays at $80,000, but your future income rises to $40,000 Future Consumption Real Interest Rate 104,000 61,000 51,500 40,000 20,000 50,000 80,000 Savings = 20,000 Savings 60,000 A rise in future income lowers savings

43. Suppose that your current income rises to $100,000, AND your future income rises to $40,000 Real Interest Rate 104,000 71,500 51,500 40,000 50,000 70,000 100,000 Savings = 30,000 Savings A permanent rise in income has no effect on savings

44. Recall the production function discussed earlier Labor Output Capital Productivity Typically the production function used is Cobb-Douglas Capital’s Share of Income Labor’s Share of Income

45. The investment decision is based on changing the capital stock holding employment fixed. Note that capital can’t be adjusted instantaneously. MPK=2 2 The Marginal Product of Capital (MPK) measures the change in production associated with a small change in the capital stock 10 MPK=10 As capital increases (given a fixed labor force), capital productivity declines!! 1 1

46. Suppose that an investment opportunity costs $100. This project will generate $25 in revenues per year (MPK), but will depreciate at 10% per year. Assume that the interest rate is 5% What’s the cost of capital? Borrow $100 Buy Capital (or use retained earnings) Capital is worth $90 Interest owed = $5 Install Capital 1 Year Now Use capital to produce output Cost: .05($100) + .10(100) = $15 Depreciation expense Lost interest

47. Suppose that an investment opportunity costs $100. This project will generate $25 in revenues (MPK), but will depreciate at 10% per year. The interest rate is 5% We will purchase capital as long as the benefits at the margin are greater than the cost. (Expected) future marginal product of new capital once installed User cost of capital

48. The optimality condition for capital gives us our “target” capital stock. To find investment, we need to remember that capital evolves according to Target Capital Stock MPK = UC Current Investment Current Capital Stock Annual Depreciation Rate We need to solve for the level of investment needed to reach our target capital stock

49. Example: For the production function given above, at a user cost of 15, 5 units of capital are needed

50. Investment demand records the by the firm at every real interest rate Real Interest Rate Investment