2. FIN 30220: Macroeconomic Analysis Capital Markets

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

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

5. 20102011 Total Employment 130M The US Economy Private Nonresidential Fixed Assets $16,946B Private Nonresidential Fixed Assets $17,346B GDP = $14,500B 2010 Consumption$10,200B Investment$1,800B Government$3,000B Net Exports-500B$ 2010 Current Capital$16,946 Depreciation$1,400B (8%) Gross Investment$1,800B Net Investment$400B Total Employment 132M

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

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

8. 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) Real interest rate Bond Price

9. 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

10. 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. $18,141,000,000,000.00 As of February 2015, total debt of the US government was equal to $13,038,000,000,000.00$5,103,000,000,000.00 Intergovernmental Debt (one branch of government borrowing from another – not “real” debt) Debt held by the public (net debt) measures outstanding government securities in financial markets

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

12. today90 days 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 Pay $997Receive $1,000 What is your (annualized) return on the bond? Bond Equivalent Yield Discount Yield

13. today90 days Receive $1,000 Suppose you required a 2% annualized return (Bond Equivalent Yield). What would you be willing to pay? Pay Price P Today ( 995 4/32) We could do the same calculation in reverse. Consider a 90 Day T-Bill with a face value of $1,000

14. today90 days Receive $1,000 Suppose you required a 2% annualized return (Discount yield). What would you be willing to pay? Pay Price P Today We could do the same calculation in reverse. Consider a 90 Day T-Bill with a face value of $1,000

15. today90 days Bond Prices vs. Bond Yields Receive $1,000 Note that there is a negative relationship between prices and yields Pay Price P Today As yields go up, prices go down! or

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

17. A yield curve represents the average annual returns for securities of different maturities. Now1 Year2 Years4 years3 Years Average annual return on a 1 year bond purchased today Average annual return on a 2 year bond purchased today Average annual return on a 3 year bond purchased today Average annual return on a 4 year bond purchased today These interest rates are referred to as “spot interest rates”.

18. Now1 year 2 years 4 years 3 years 2 % 2.5% 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 Consider two investment strategies For these strategies, to pay the same return: Suppose we observe a current set of spot rates

19. Now1 year 2 years 4 years 3 years 2% 2.5% 3% Forward rates are not observed, but can be calculated given any two spot rates Return on a 1 year security Purchase date is 1 year from today

20. Given any yield curve, we can calculate an expected path for forward rates: Now1 Year2 Years4 years3 Years

21. Now1 Year 2 Years 4 years3 Years 2%2.5% 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: Alternatively, suppose we know the path of forward rates…

22. Given a set of forward rates, we can calculate the implied spot rates Now1 Year2 Years 4 years 3 Years 2% 2.5% 3% 3.5% Spot rates are based on the geometric average of expected future rates

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

24. Suppose that expected future rates were expected to be constant Now1 Year2 Years 4 years 3 Years 3% The yield curve is flat!

25. For these strategies, to pay the same return.. An upward sloping yield curve suggests that the market expects interest rates to rise in the future…with one small problem.. 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 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

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

27. Now1 Year Pay $945 CPI = 100 Receive $1,000 CPI = 104 Suppose that you invest $945 in a one year, $1,000 T-Bill. Prices are listed below as well Now, lets convert your $1,000 to current prices and redo the yield This is your inflation adjusted, or, real return

28. Recall that nominal (currency) variables are meaningless without some mention of prices. The same hold for interest rates. Now1 Year Pay $945 CPI = 100 Receive $1,000 CPI = 104 Inflation Rate = 4% Exact Method Approximation

29. US Real Returns (1948-2014)

30. Now1 Year Pay $945 CPI = 100 Receive $1,000 At the time you bought the asset, you did not know what inflation would be. Your Expectation: CPI = 102 Actual: CPI = 104 Ex Ante Expected inflation Ex Post Actual inflation We can only measure ex post real interest rates!!

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

32. 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).

33. $50,000 Without capital markets, consumption equals income at every point in time $50,000 With capital markets, total lifetime consumption equals total lifetime wealth Savings < 0 (Borrowing) Savings > 0 Saving and Consumption

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

35. 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

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

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

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

39. 99,047 104,000 20,000 80,000 Current Consumption Future Consumption Savings Real Interest Rate 50,000 51,500 Savings = 30,000

40. 99,047 104,000 20,000 80,000 Current Consumption Savings Real Interest Rate 50,000 51,500 Suppose that the interest rate increases to 8%... Substitution effect: As interest rates rise, current consumption becomes more expensive – spend less today! (Save More) Income Effect: As interest rates rise, you earn more interest income – spend more today! (Save Less) Substitution effect Income Effect 40,00060,000

41. 99,047 104,000 20,000 80,000 Savings Real Interest Rate 40,000 We typically assume that the substitution effect is dominant…a rise in the real interest rate increases savings. 62,000 Savings = 40,000

42. 104,000 20,000 Future Consumption Savings Real Interest Rate 50,000 51,500 Suppose that your current income increases to $100,000… 100,00060,000 Savings = 40,000 62,000 A rise in current income increases savings

43. 104,000 20,000 Future Consumption Savings Real Interest Rate 51,500 Suppose that your current income stays at $80,000, but your future income rises to $40,000 Savings = 20,000 40,000 A rise in future income lowers savings 80,00050,000 60,000 61,000

44. 104,000 Savings Real Interest Rate 51,500 Suppose that your current income rises to $100,000, AND your future income rises to $40,000 Savings = 30,000 40,000 A permanent rise in income has no effect on savings 100,00050,000 71,500 70,000

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

46. As capital increases (given a fixed labor force), capital productivity declines!! The Marginal Product of Capital (MPK) measures the change in production associated with a small change in the capital stock 11 10 2 MPK=2 MPK=10 The investment decision is based on changing the capital stock holding employment fixed. Note that capital can’t be adjusted instantaneously.

47. Now 1 Year 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? Capital is worth $90 Interest owed = $5 Use capital to produce output Borrow $100 Buy Capital (or use retained earnings) Install Capital Cost:.05($100) +.10(100) = $15 Lost interest Depreciation expense

48. 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. User cost of capital (Expected) future marginal product of new capital once installed

49. 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 Capital Stock Current Investment Annual Depreciation Rate We need to solve for the level of investment needed to reach our target capital stock

50. CapitalOutputMPK 1140 218040 321030 423020 524515 62505 Example: For the production function given above, at a user cost of 15, 5 units of capital are needed

51. Investment demand records the by the firm at every real interest rate Investment Real Interest Rate CapitalOutputMPK 1140 218040 321030 423020 524515 62505

52. Changing the interest rate allows us to sketch out investment demand Investment Real Interest Rate CapitalOutputMPK 1140 218040 321030 423020 524515 62505

53. Investment Real Interest Rate CapitalOutputMPK 1120 214020 315515 416510 51705 61722 Changing production values allows us to sketch out shifts in investment demand

54. Anything that raises (lowers) the productivity of capital will increase (decrease) investment demand The productivity of capital is influenced by  Employment (+)  Technology (+)

55. Finally, we need to find an equilibrium in the capital market – a real interest rate that equates savings (inflow into financial sector) and Investment (outflow from financial sector) Labor Markets determine current output (Income) Given Current Income and the current capital stock, Capital markets determine Savings, Investment, and the real interest rate

56. We need to make assumptions about the evolution of productivity (and, hence, income) to know what happens to savings. Let’s suppose that productivity evolves according to an autoregressive process Productivity shock Persistence parameter

57. Suppose that the economy experiences a temporary increase in productivity Increase in productivity For a given level of capital and labor, a rise in productivity raises output

58. Suppose that the economy experiences a temporary increase in productivity With an increase in both the supply of loanable funds (savings) and the demand for loanable funds (investment), the interest rate change is ambiguous, and the quantity of both savings and investment increase

59. An increase in productivity that is perceived to be permanent will have minimal effect on savings (permanently higher income raises consumption), but investment increases Interest Rates increase Increase in productivity

60. Just the facts ma’am. Capital Markets and the business cycle Given the mechanics of capital markets, what relationships would we expect to see between savings, investment, interest rates, and output? CorrelationOutput Savings+ Consumption+ Investment+ Interest Rates?

61. GDP vs. Savings (% Deviation from trend) Correlation =.77 GDP (% Deviation from Trend) Savings (% Dev. From trend)

62. GDP vs. Consumption (% Deviation from trend) Correlation =.78 GDP/Consumption (% Dev. From trend)

63. GDP vs. Investment (% Deviation from trend) Correlation =.83 GDP (% Dev. From Trend) Investment (% Dev. From Trend)

64. GDP vs. Interest Rates (% Deviation from trend) Correlation =.42 The high, positive correlation suggests shocks that are more permanant

65. Example: Oil Price Shocks in the 1970’s Dollars per Barrel 1973 Arab Oil Embargo (Permanent Shock) 1979 Iranian Revolution (Temporary Shock)

66. We can view the rapid rise in the price of oil as a decline in productivity… With a temporary decline, we get a drop in savings and investment. The new equilibrium interest rate is ambiguous. With a temporary decline, we get a drop in investment. The new equilibrium has lower interest rates

67. Investment (% Dev. From Trend ) Real Interest Rate 1973 Arab Oil Embargo 1979 Iranian Revolution