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More on risk An introduction to bonds

“You must risque to win” --- Andrew Jackson 7 th US president Nicknames: King Mob, Old Hickory, The Hero of New Orleans. More on risk An introduction to bonds. Monte Carlo simulation How do bonds work? What are the risks of bond ownership Real options

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More on risk An introduction to bonds

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  1. “You must risque to win” --- Andrew Jackson 7th US president Nicknames: King Mob, Old Hickory, The Hero of New Orleans More on riskAn introduction to bonds Monte Carlo simulation How do bonds work? What are the risks of bond ownership Real options If time permits at the end of the lecture, I can take some questions for Test 1

  2. Monte Carlo simulation • I could further complicate the previous examples • More possible quantities sold • 300, 301, 302, …, 898, 899, 900 • More possible ACs • $350, $351, …, $598, $599, $600 • More possible prices • $800, $801, …, $1198, $1199, $1200

  3. These variables could be correlated with each other • Instead of having clear possible outcomes, it may be that other factors need to be considered • Will AC be higher with higher outputs if there is a labor shortage? • Will price be lower with higher outputs due to increased competition • Can we find a new technique to lower AC if we have a low production quantity

  4. How can we predict expected revenue? • Monte Carlo simulation uses repeated draws to come up with expected revenue • How does Monte Carlo simulation work? • We let computers do the work for us

  5. What is Monte Carlo simulation? • Enter the possible outcomes, including the distribution for each variable • Note that some variables could be correlated (see two slides before for examples) • Draw one outcome, given the probabilities of all possible outcomes • Repeat the previous step, usually thousands or millions of times • Calculate the expected NPV of the project from the draws you made by averaging all outcomes

  6. Back to the housing market • Monte Carlo simulations are sometimes done to calculate the expected value of different types of loans • Loans that were made 10 years ago likely ignored the possibility of very bad outcomes that actually occurred • Overestimated the NPV of these loans • These banks made more high-risk loans than they should have to maximize their expected profits

  7. Drawback of Monte Carlo simulation • Just like any technique we have used, the assumptions are important to give us reliable results • Increased complexity of Monte Carlo simulations make understanding the assumptions more difficult • Correct assumptions are crucial to any analysis involving risk

  8. What is coming up? • Real options • Can we create riskier situations in our favor? • How do we value bonds? • Are bonds completely safe investments? • Why/why not?

  9. Buyer beware:Fake bonds seized, Feb. 2012 One form of risk is authenticity of what you buy Picture from AP, accessed from http://www.bloomberg.com/news/2012-02-17/italy-police-seize-6-trillion-of-fake-u-s-treasury-bonds-in-switzerland.html

  10. Look familiar? This is a picture of a real $100,000 bill

  11. Bad returns for US government bonds continue • July 1, 2014/Jan. 26, 2015/July 20, 2017 annual returns • 3-month bonds at 0.02%/0.02%/1.15% • $1,000,000 invested for 3 months at 0.02% will earn less than $50 in interest • Better than in late December, 2011  <0.01% • 1-year bonds at 0.11%/0.18%/1.22% • 5-year bonds at 1.66%/1.36%/1.82% • 20-year bonds at 3.13%/2.14%/2.60% • CPI index shows annual inflation at 0.7-2.1% since 2012 Returns source: https://www.oanda.com/forex-trading/analysis/economic-indicators/united-states/rates/yield-curve Inflation source: http://www.usinflationcalculator.com/inflation/current-inflation-rates/

  12. Why so low? • Remember that there are few safe investments with any reasonable return • People want to earn some interest on their money • Most bank interest rates are very low • Even with a $25,000 balance, you may only get 0.10-0.30% effective annual interest rate (also referred to as APY)

  13. How do bonds work? • Consider a bond to be a loan from a firm to a bondholder • The firm can offer two types of paybacks • Pay interest each year • “Coupons” • Pay all of the interest when the life of the bond is over • “Zero-coupon bonds”

  14. A bond with a coupon • In theory, a bond can have a life of any length • In reality, bonds rarely last for more than 30 years • In our example here, we will assume a bond sells for $5,000 (face amount) with a yield of 12%, for 20 years • Yearly coupon interest of $600

  15. A bond with a coupon • What are the cash flows? • The bondholder lends $5,000 in year 0 to the firm • The bondholder receives $600 in yearly interest in years 1-20 • The bondholder receives an additional $5,000 in year 20, since the bond’s life is over How do we think of bonds? Two ways…

  16. A bond as a loan • Notice that the cash flows of a loan could be treated with the following explanation • You deposit $5,000 in a bank • You receive $600 in yearly interest that you do NOT reinvest (coupon payments) • After 20 years, you withdraw your $5,000

  17. Present value analysis • You could also value the future payments using present value analysis • If you give up $5,000 today, you want $5,000 back (PV) in the future • Annuity present value • $600  (1 – 1/1.1220)/.12 = $600  7.4694 = $4482 • Value of $5,000 paid back 20 years from now • $5,000 / 1.1220 = $518 $5,000 total in PV

  18. A zero coupon bond:A typical example • A company offers to sell a bond in which the only payment to be made is $5,000 in 10 years • Note that this is a zero coupon bond • The selling price today is $2,112 • What is the yearly interest rate? • This is also referred to as the yield to maturity • Invest $2,112 today • Receive $5,000 in 10 years • To calculate the yearly interest rate, we need to solve for • $5,000 / (1 + y)10 = $2,112 • (1 + y)10 = 2.3674 • (1 + y) = 1.09 • y = 0.09 = 9%

  19. Are bonds completely safe investments? • Partially yes • Assuming that the lender does not default on a loan, you are guaranteed a rate of return over the life of the bond • When you buy a bond when it is first distributed, the lender cannot later decrease the interest rate • Partially no • If interest rates go up, the value of your bond goes down • The lender will not voluntarily increase the interest rate over the life of the loan

  20. Interest rate risk • Suppose that you invest in a one-year bond today • You will be paid $1,000 one year from now • You accept a yearly interest rate of 5% • You will pay $952.38 today • Let’s assume that you can re-sell the bond at any point in the next year

  21. Interest rate risk • You walk away from the bond seller and you find out that the bond you just bought is now offering a yearly interest rate of 8% • You are happy because you have a higher interest rate Hold on: You paid $952.38 when you could have paid only $925.93 when the interest rate went up

  22. Interest rate risk • When interest rates fluctuate, you want to lock in… • …a high interest rate when you are buying bonds • …a low interest rate when you are selling bonds • The promised interest is lower when interest rates are lower

  23. What if the length of the loan was longer? • Suppose that we had the same scenario as before, except that the length of the life of the bond is 10 years • Assume zero coupons • You bought for $613.91 at a 5% effective annual interest rate • You could have bought for $463.19 at an 8% effective annual interest rate • Note that the longer the life of the bond, the greater the interest rate risk

  24. Before we finish… • Real options

  25. Real options • So far, I have hailed the advantages of NPV • However, I have ignored real options in calculating NPV • A real option is a potential adjustment that can be made to a project to make it more or less profitable • We will only care about trying to make more profit, since we will not want to enact adjustments that will lead to lower profit • Exception: Some real options are involuntary

  26. We should always incorporate real options in NPV • Suppose I wanted to open a new coffee shop • Success only occurs with probability 0.2 • r = 12.5%

  27. Forecasts • Successful forecast (probability 0.2) • Pay $100,000 in costs today • Annual cash flows of $20,000 per year (starting next year) • NPV of annual cash flows is $160,000 • NPV is $60,000 • Pessimistic forecast • Pay $100,000 in costs today • Annual cash flows of $8,000 per year (starting next year) • NPV of annual cash flows is $64,000 • NPV of a loss of $36,000 NPV = -$16,800

  28. What is the real option here? • Suppose that in the optimistic case, someone will offer me $1,000,000 ten years from now for the right to expand nationwide • 20% probability of this occurring • 20% of $1 million is $200,000 • We need to incorporate this in the cost-benefit analysis • We need to discount a $200,000 payment ten years from now • $200,000 / 1.12510 = $61,589 • Our NPV with this real option included is –$16,800 + $61,589 = $44,789

  29. Abandoning a project • Sometimes, we must abandon a project because the market conditions change • Suppose that I have already invested $10,000 in my coffee shop • At this point, Starbucks buys out another emerging coffee shop chain that eliminates my real option, even if my company is successful

  30. How to get to a new calculation • Remember that the $10,000 is a sunk cost at this point • No real options left • Good outcome (20% prob.) • Pay $90,000 today • NPV of annual cash flows is $160,000 • Bad outcome • Pay $90,000 today • NPV of annual cash flows is $64,000 • NPV is –$6,800  STOP!

  31. What should I do? • Despite the money already spent, I should decide to stop investing money in the business and go do something else

  32. Decision trees • When analyzing investments, we can use a decision tree to help us determine what steps we should take • We can work backwards to determine what course of action to take

  33. Making calculations for a decision tree • Let’s look at GM • Suppose you can buy a bond in Year 0 for $500 that promises to pay a $100 coupon per year for three years, starting in Year 1, along with an additional $600 payment in Year 3 • Your annual discount rate is 12% • Risk should be incorporated into the discount rate • You determine that GM will go out of business with probability 0.2 between Year 1 and Year 2 • If GM goes bust, you receive $350 two years from today • Should you buy?

  34. Calculating NPV • NPV of bond if GM stays in business • –$500 + $100 (1/1.12) + $100 (1/1.12)2 + $100 (1/1.12)3 + $600 (1/1.12)3 = $167.25 • NPV of bond if GM goes out of business • –$500 + $100 (1/1.12) + $350 (1/1.12)2 = –$131.70

  35. Decision tree Squares depict decision points Circles depict information Let’s work backwards… 0.8 * $167.25 + 0.2 * (-$131.70) = $107.46

  36. What kinds of bonds are there? Barry Bonds 007 (James Bond)

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