1. Finance & Investments
Lecturer: Todd Kaplan

2. Introduction
Finance is one of the more successful offshoots of economics.
Econometrics, Microeconomics and even Behavioural Economics have all had a strong influence on the field.
We hope to cover some of the fundamental concepts (rather than the institutional detail).

3. Before I forget Web page: econ.haifa.ac.il/~todd/finance.html
Recommended book “Investment Analysis”, by Gareth Myles (unpublished).
For the course, there will be homework to do (maybe two assignments) 15% plus a test at the end 85%.

4. Fixed-Income Securities
Securities that promise to pay a fixed income and so are known as fixed-income securities.
These include bonds and mortgages.
Once thought to be boring. Now it is where a lot of action is.

5. Future Values Example - FV
What is the future value of £100 if interest is compounded annually at a rate of 6% for five years?

6. Manhattan Island Sale
(Q1.1) Peter Minuit bought Manhattan Island for £16 in Was this a good deal?
To answer, determine £16 is worth in the year 2001, compounded at 8% and 5%.

7. Present Values Present Value: Value today of a future cash flow
Discount Rate: Interest used to calculate value of future cash flows.

8. Present Values

9. Present Values Example
(Q1.2)You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years?

10. Time Value of Money (applications)
The PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable.

11. Arbitrage
(Q1.3) You are given the following prices Pt today for receiving risk free £1 payments t periods from now.
If you can costlessly buy or sell, how would you make a lot of money? T= 1 2 3
Pt=
0.95
0.9

12. PV of Multiple Cash Flows
Example
(Q1.4) Your auto dealer gives you the choice to pay $15,500 cash now, or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money is 8%, which do you prefer?

13. PV of Multiple Cash Flows
PVs can be added together to evaluate multiple cash flows.

14. Review Question
(Q1.5) A consultant is paid a fee at the end of each of the next 5 years. At the 21% annual interest rate the present value of the payment is $1m. The contract is then renegotiated. Each payment remains the same but the first is received after 6 months and the rest follow at 12 monthly intervals. What is the new PV?

15. Perpetuities & Annuities
Perpetuity
A stream of level cash payments that never ends.
Annuity
Equally spaced level stream of cash flows for a limited period of time.

16. Perpetuities & Annuities
Example - Perpetuity
(Q1.6) In order to create an endowment, which pays £100,000 per year, forever, how much money must be set aside today in the rate of interest is 10%?

17. Perpetuities & Annuities
Example - Perpetuity
In order to create an endowment, which pays £100,000 per year, forever, how much money must be set aside today in the rate of interest is 10%?

18. Perpetuities & Annuities
PV of Annuity Formula
C = cash payment
r = interest rate
t = Number of years cash payment is received

19. Question
A recent article in the NY times mentioned that a college degree increases one’s earnings by one million dollars (in the US).
(Q1.7) How much should one be willing to pay for college tuition?

20. Mortgage payments (Q1.8) You want to buy a home for £100,000.
Natwest offers you a mortgage: 0 down, 10% a year for 25 years.
How much must you pay per year?

21. Mortgage Question
(Q1.9) Assume mortgage interest is about 6% per year and mortgages last 25 years.
If average mortgages is about 4 times annual income, what percent of income goes to the mortgage payment?

22. Compounding
(Q1.10) Natwest is offering loans at 10% interest compounded quarterly.
Barclays is offering loans at 10.5% interest compounded annually.
Which would you take?

23. Compounding
The value of $100 at 10% interest, Compounded m times a year.

24. Compounding Formula 10.51709180756477 General Formula is
What is the limit as n-->Infinity
Continuous is
Why? Look at % increase (slope/value)
What is continuous rate for 10% annual?

25. Questions
(Q1.11) How long would it take to double your money? (Hint: Log(2)≈0.7, actually .69)
(Q1.12) I am hoping my savings will quadruple by the time I retire at the age of 75. What interest rate do I need?

26. Saving for a baby’s pension
(Q1.13)Say you have a new baby and you want to put money aside for the baby’s pension.
Assume the baby will retire years of age.
How many times will the money double?
So the money is simply 2r times the investment.
How much do you need for a million dollar pension?
Million is roughly 210 times 1000.
One needs 210-r times 1000.

27. Save and Retire.
(Q1.14) You plan to save £4,000 every year for 20 years and then retire. Given a 10% rate of interest, what will be the FV of your retirement account?
(Q1.15) If you expect to live for another 20 years, how much would a pension that pays £10,000 each year cost at 6% interest?

28. Growth and Perpetuities
(Q1.16) What is the present value of a perpetuity whose payment grows at a rate of (1+g) per year?
(Q1.17)If you expect to live for another 20 years, how much would a pension that pays £10,000 each year cost at 6% interest and grows with inflation which is at 2%?
1.16 c/(r-g) (1-(1+g)/(1+r))^20)=134k

29. Bonds
Terminology
Bond - Security that obligates the issuer to make specified payments to the bondholder.
Coupon - The interest payments made to the bondholder.
Face Value (Par Value or Maturity Value) - Payment at the maturity of the bond.
Coupon Rate - Annual interest payment, as a percentage of face value.
Callable – The issuer can repay the bond before maturity.

30. Bonds
WARNING
The coupon rate IS NOT the discount rate used in the Present Value calculations.
The coupon rate merely tells us what cash flow the bond will produce.
Since the coupon rate is listed as a %, this misconception is quite common.

31. Bond Pricing
The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.

32. Bond Sensitivity A zero coupon bond pays £10000 in 10 years time.
(Q1.18) What is the PV of the bond if interest is 10% annual?
What is the PV of the bond if interest falls to 9% annual?

33. Bond Pricing
The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.

34. Bond Pricing
(Q1.19) What is the price of a 6 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 5%.
What is the price if the return is 6%

35. Bond Yields
Current Yield - Annual coupon payments divided by bond price.
Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price.

36. Bond Yields Calculating Yield to Maturity (YTM=r)
If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.

37. Callable bonds
(Q1.20) Say Haifa offers a bond with a yield of 10% for two years. It has a face value of $1000 and coupons of $100 paid annually. What is the price?
Now say the yield is either 11% or 9% in year 2 with a 50% chance of each. What is the price?
Now, in addition, say the bond is callable. When would Haifa call the bond? Shoud the price be higher or lower than before? What is the price?

38. Junk bond Risk
Premium Bond
Discount Bond

39. Interest Rate Risk
30 yr bond
3 yr bond

40. Default Risk
Credit risk
Default premium
Investment grade
Junk bonds

41. Default Risk

42. Corporate Bonds Convertible bonds
Green [1984] says they are useful to protect bondholders from the shareholders’ increasing the risk.
Brennan Kraus [1987] say they signal share volatility.
Stein [1992] says they can signal that the board thinks the value of the firm is higher than the market price (delaying financing).

43. Green [1984]
Say a company has issued 1 million dollars worth of stock and 1 million dollars worth of bonds.
Total value of the company is 2 million dollars. (NOT THE MARKET CAP)
Say with the current strategy a 50% the company would be worth 1.5 million and 50% worth 3 million in a year.
Note that the interest on the bonds is 10% (and they will be paid first).
What will the stock be worth on average in a year?
The company can change strategy so that the company would be worth either 0 with probability 75% or 6.6 million with probability 25%.
If it does so, what would the stock be worth on average in a year?
Will the stockholders take such a strategy?
If the company were a private company, which strategy would it choose?
Would this make selling the bonds more difficult?
Say there are 10,000 shares. Each $200 bond is convertible into a share next year. What would happen if the strategy isn’t changed? What would happen if the strategy is changed?
Which strategy would the stockholders choose?

44. Brennan Kraus [1987]
There are two types of firms: volatile and non volatile.
A bond holder wants 10% interest from a volatile firm and only 5% from a non volatile firm.
Say the CEO is a major shareholder and knows the firm’s volatility.
The firm has a large market cap and wants to raise 1 million in bonds.
The current stock price is $100. A volatile firm has 5% chance of hitting $300 in one year. A non-volatile firm has a 0% chance of going over $150 in one year.
The CEO of the non volatile firm offers a convertible bond at a 5% yield that is convertible at $150 for a year (for each $100).
Would the CEO of the volatile firm want to duplicate this?
Would the potential bondholders buy this offering w/o knowing beforehand the volatility?

45. Stein [1992] More or less adds equity to Brennan Krauss.
A firm is either undervalued, overvalued or slightly overvalued.
A firm needs to raise 1 million dollars.
The firm can raise money by a normal bond, a convertible bond, or selling equity.
An overvalued firm will sell equity.
An undervalued firm will simply offer a bond at a higher rate of interest.
A slightly overvalued firm will offer a convertible bond.
Why doesn’t an overvalued firm want to sell a bond?
Why doesn’t an undervalued firm want to sell equity or a convertible bond?
Why doesn’t a slightly undervalued firm want to equity or a regular bond?

47. The Yield Curve
Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date.
Yield Curve - Graph of the term structure.
(see finance.yahoo.com)
Q1.21: If you knew interest rates won’t change from now until one year from now, what would that mean about the yield curve of US treasury bonds?

48. Overview of Term Structure
The relationship between yield to maturity and maturity.
Information on expected future short term rates can be implied from yield curve.
The yield curve is a graph that displays the relationship between yield and maturity.

49. Yield to Maturity and Prices and Prices on Zero-Coupon Bonds ($1,000 Face Value)

50. Short Rates versus Spot Rates

51. Forward Rates from Observed Rates
fn = one-year forward rate for period n
yn = yield for a security with a maturity of n

52. Example of Forward Rates
(Q1.22) A 4 year bond has an 8.00% yield.
A 3 year bond has a 7.00% yield.
What is the forward rate f4 = ?
(1.08)4 = (1.07)3 (1+fn)
(1.3605) / (1.2250) = (1+fn) OR fn = or 11.06%
Note: this is expected rate that was used in the prior example.

53. Theories of Term Structure
Expectations
Liquidity Preference
Upward bias over expectations

54. Expectations Theory
Observed long-term rate is a function of today’s short-term rate and expected future short-term rates.
Long-term and short-term securities are perfect substitutes.
Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates.
What does an upward sloping yield curve imply about expectations? Downward sloping?

55. Liquidity Premium Theory
Long-term bonds are more risky.
Investors will demand a premium for the risk associated with long-term bonds.
The yield curve has an upward bias built into the long-term rates because of the risk premium.
Forward rates contain a liquidity premium and are not equal to expected future short-term rates.

56. Liquidity Theory
Todd has $1000 to invest. He knows he is going to need the money in 1 year’s time.
There are two investments.
A one-year bond with yield of 5%.
A two-year bond with yield of 5%.
The price of the two-year bond after one year has a 50% of being $1000 and a 50% chance of being $1100.
Which should he invest in?

57. Yield Curves (with Liquidity Premiums)

58. Supply Side
If yield is lower for 3 month bonds, why wouldn’t those selling the bonds only sell 3 month bonds?
Think Lehman brothers.
Think Greece.

59. Market Segmentation (Preferred Habitat)
Perhaps pension funds want 30 year bonds and other investors want shorter bonds.
Not enough market forces driving the yield curve to reflect the expectations.

60. Price Volatility of Long-Term Treasury Bonds

61. Yields on 10-Year versus 90-Day Treasury Securities: Term Spread

62. Skip this…. What should the difference be?
r1=0.5. r2 is either 0 or 1 with 50% chance of each.
Jim has $1000 to invest. Sean has $1000 to invest.
Jim invests in short term bonds. Sean in long term bonds.
What can they expect at the end of 2 periods?
Sean gets (1+y)2*1000. Jim 50% of the time gets and 50% gets 3000.
If there is risk-neutrality, on average these should be the same or (1+y)2=2.25, which implies y=.5.
They are the same as long as E[r2]=r1.
It could be a slight bit less (E[y]<=E[r]).
Geometric mean vs. arithmetic.

63. Orange County California
Robert Citron was called a genius, but in 1994 the lost $1.7 billion of Orange County’s $7.4 billion portfolio. He was not supposed to be taking risks.
The whole portfolio was in US treasury bonds. (see “Big Bets Gone Bad” by Phillippe Jorion, Academic Press).
Citron pled guilty to six felony counts and three special enhancements. Charges also included filing a false and misleading financial summary to participants purchasing securities in the Orange County Treasury Investment Pool.
While in bankruptcy, every county program budget was cut, about 3,000 public employees were discharged and all services were reduced. Citron was ordered to serve five years of supervised probation, and to perform 1000 hours of community service. Citron did not serve any time in prison.
What happened?

64. US Bonds are Risky
Notice the jump
US Federal Funds Rate

65. The bet.
Citron basically used his bonds as collateral for loans to buy more bonds.
This essentially lengthened the average time to maturity of his portfolio.
As interest rates went down it went up in value. As interest rates rose they went down.