P1.T3. Hull, Chapter 5. Bionic Turtle FRM Video Tutorials. By: David Harper CFA, FRM, CIPM

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1 P1.T3. Hull, Chapter 5 Bionic Turtle FRM Video Tutorials By: David Harper CFA, FRM, CIPM Note: This tutorial is for paid members only. You know who you are. Anybody else is using an illegal copy and also violates GARP s ethical standards. 1

2 P1.T3. Hull, Chapter 5 Markets and Products 3.b Agenda Hull, Options, Futures, and Other Derivatives, 8th Edition Chapter 5: Determination of Forward and Futures Prices 2

3 P1.T3. Hull, Chapter 5 Related Learning Spreadsheets Workbook Exam Relevance (XLS not topic) Spreadsheets T Commodity Carry High Hull s Cost of Carry Models Note: If you are unable to view the content within this document we recommend the following: MAC Users: The built-in pdf reader will not display our non-standard fonts. Please use adobe s pdf reader ( PC Users: We recommend you use the foxit pdf reader ( or adobe s pdf reader ( Mobile and Tablet users: We recommend you use the foxit pdf reader app or the adobe pdf reader app. All of these products are free. We apologize for any inconvenience. If you have any additional problems, please Suzanne at suzanne@bionicturtle.com. 3

4 Hull, Chapter 5: Determination of Forward and Futures Prices 4

5 Differentiate between investment and consumption assets. Investment Consumption Held for investment purpose Does not need to be solely for investment: could also have consumption purposes (e.g., silver) Primarily for consumption 5

6 Differentiate between investment and consumption assets. Investment Consumption [Theory] No-arbitrage implies forward is a function of spot price Because of convenience yield, forward price is not a simple function of spot 6

7 Define short selling and short squeeze. Time 0 Borrow shares, Sell shares Cash Flow + Price 1 Pay dividend - Dividend 2 Buy shares to close short position Profit in short sale (no TVM) = - Ending Price Initial Price (Ending Price + Dividend) Short squeeze: Contract is open Broker runs out of shares to borrow Investor is forced to cover (close out) position 7

8 Discuss the differences between forward and futures contracts and explain the relationship between forward and spot prices. Forward Trade over-the-counter Not standardized One specified delivery date Settled at contract s end Delivery or final cash settlement usually occurs Forward vs. Futures Contracts Futures Trade on an exchange Standardized contracts Range of delivery dates Settled daily Contract usually closed out prior to maturity 8

9 Cost of Carry Cost of carry = cost of financing + storage income received Forward price = Cost of carry Convenience Yield Risk-free Rate (r) Storage Cost (U, u) Income/ Dividend (q) Convenience (y) Forward (F 0 ) Spot (S 0 ) Time (T) 9

10 Discuss differences between forward and futures contracts & explain the relationship between forward and spot prices. Cost of carry = cost of financing + storage cost income received F F S e S e ct Forward: End of Contract Futures: Daily Settlement Cash Flow Volatility cy T Investment Asset Consumption Asset 10

11 Calculate forward price, given underlying asset s price, McDonald s Example in Chapter 5: Corn spot, S(0), is $2.50 Interest rate, r, is 6.0% per annum with continuous compounding Storage cost is 1.5% per month One-year forward price Cost of Carry: Consumption Commodity (corn) with storage but no convenience McDonald s Corn Spot, S(0) $2.50 Time to maturity (months) 12 Interest rate (per annum) 6.00% Interest rate (per month) 0.50% Storage costs, as % (per month) 1.50% Yield/Dividend, as % (per month) Convenience Yield, as % (per month) 0% Implied Forward Price (F0) $3.18 F S e ( ruy) T F0 $2.50e F0 $2.50e (0.5% 1.5%)12 (6% 18%)1.0 11

12 Calculate forward price, given underlying asset s price, Hull s long forward contract to purchase coupon-bearing bond (Hull 5.5) Current bond price, S(0), is $ Forward contract matures in nine (9) months Coupon payment of $40.00 expected after four (4) months Risk-free rate: 3.0% at 4 months, and 4% at 9 months Cost of Carry: Investment commodity (bond) with income but no storage Hull s Bond Spot, S(0) $ Time to maturity (months) 9 Interest rate (per annum) 4.00% Interest rate (per month) 0.33% Storage costs, as % (per month) 0% Yield/Dividend, PV of lump-sum $39.60 Convenience Yield, as % (per month) 0% Implied Forward Price (F0) $ F ( S I) e rt I 3% 4/12 $40 e $39.60 F F e e 4% 9/ % 9 12

13 Calculate forward price, given underlying asset s price, Cost of Carry Red are ownership costs increase forward price (rate, storage) Blue are ownership benefits decrease forward price (income, convenience) McDonald Hull Stock Long Bond Corn Forward Forward Spot (S0) $2.50 $40.00 $ Time to maturity (months) Interest rate (per annum) 6.00% 5.00% 4.00% Interest rate (per month) 0.50% 0.42% 0.33% Storage costs, as % (per month) 1.50% 0.00% 0.00% Yield/Dividend, as % (per month) Convenience Yield, as % (per month) 0% 0% 0% Implied Forward Price (F0) $3.18 $40.50 $ Income/Cost as Lump Sum FV of income/cost (+ income, - cost) $40.00 Time to Lump Sum (months) 4 Discount Rate 3% PV of Income (I) $0.00 $0.00 $

14 Calculate the forward price, given asset s price, with/without short sales and/or consideration to income/yield. Consumption Commodity F S e ( ruy) T constant rates as % u = storage costs y = convenience yield ( ) ( r y ) T F S U e Present values U = Present value, storage costs 14

15 Calculate the forward price, given asset s price, with/without short sales and/or consideration to income/yield. Investment Asset (Commodity) F S e ( r q) T constant rates as % q = income (dividend) F ( S I) e rt Present values I = Present value, income 15

16 Please Note: Difference Between Forward Price & Forward Value Value of forward is Zero at Inception! Price of forward = F S e ( rq) T Value of forward f ( F K) e 0 rt Fluctuating (Changing) Constant 16

17 Question A stock s price today is $50. The stock will pay a $1 (2%) dividend in six months. The risk-free rate is 5% for all maturities. What the price of a (long) forward contract (F 0 ) to purchase the stock in one year? 17

18 Answer A stock s price today is $50. The stock will pay a $1 (2%) dividend in six months. The risk-free rate is 5% for all maturities. What the price of a (long) forward contract (F 0 ) to purchase the stock in one year? ( ) rt 0 F S I e F $ ( 0.05)(6/12) (.05)(1) ($50 [($1) e ]) e 18

19 Describe an arbitrage argument in support of these prices. S 0 F 0 rt F S U e rt F S U e Cash and carry Reverse Cash and carry 19

20 Explain the relationship between forward and futures prices. If risk-free rate is constant and same for all maturities, then forward price should equal (=) futures price Correlation of underlying asset (S) with interest rates Strongly positive: futures > forward Strongly negative: futures < forward Contract life Short: negligible Long (e.g., 10 year Eurodollar futures): can be significant 20

21 Use the interest rate parity relationship to calculate a forward foreign exchange rate. F F S e S e ( r q )T ( r r )T f 21

22 Use the interest rate parity relationship to calculate a forward foreign exchange rate units of foreign currency at time zero 1000 S(0) dollars at time zero 1000 S(0) exp(rt) at time T 1000 exp(rf T) at time T 1000 exp(rf T) F(0) at time T rf T 1000e F 1000S e F S e ( r r )T f rt 22

23 Use the interest rate parity relationship to calculate a forward foreign exchange rate. Hull s Example 5.6 Spot FX rate is USD per AUD 2-year interest rates: 5.00% in Australia (AUD) and 7.00% in U.S (USD) F S e ( r r )T e f ( 7% 5%) 2 23

24 Define income, storage costs, and convenience yield. Income Stocks paying known dividends Coupon-bearing bonds Storage costs = negative (-) income Convenience yield: the plug variable that validates the cost of carry model Impounds benefits of holding/owning the physical asset Including the real option 24

25 Calculate the futures price on commodities incorporating storage costs and/or convenience yields. Hull Hull Spot (S0) $ $ Time to maturity (months) Interest rate (per annum) 7.00% 7.00% Interest rate (per month) 0.58% 0.58% Storage costs, as % (per month) 0.00% 0.00% Yield/Dividend, as % (per month) 0.42% 0.00% Convenience Yield, as % (per month) 0% 0% Implied Forward Price (F0) $ $ Income/Cost as Lump Sum FV of income/cost (+ income, - cost) -$2.00 Time to Lump Sum (months) 12 Discount Rate 7% PV of Income (I) $0.00 ($1.86) 25

26 Define and calculate, using the cost of carry model, forward prices where the underlying asset has interim cash flows. Long Bond Forward Spot (S0) $ Time to maturity (months) 9 Interest rate (per annum) 4.00% Interest rate (per month) 0.33% Storage costs, as % (per month) 0.00% Yield/Dividend, as % (per month) Convenience Yield, as % (per month) 0% Implied Forward Price (F0) $ Income/Cost as Lump Sum FV of income/cost (+ income, - cost) $40.00 Time to Lump Sum (months) 4 Discount Rate 3% PV of Income (I) $

27 Discuss the various delivery options available in the futures markets and how they can influence futures prices. If futures price is increasing function () of time to maturity Short should deliver as early as possible. Assume delivery at beginning of period. If futures price is decreasing function () of time to maturity Short should deliver as late as possible. Assume delivery at end of period. First notice day Last trading day Last notice day Intention to deliver 27

28 Define Contango & backwardation, interpret the effect contango or backwardation may have on the relationship between commodity futures and spot prices.. Cost of carry = cost of financing + storage cost income received 28

29 Analyze the relationship between current futures prices and expected future spot prices. 29

30 including the impact of systematic and nonsystematic risk. ( ) ( r k ) T 0 T F E S e k r * ERP CAPM riskfree If the investment has positive systematic risk, the future price should be less than the expected future spot price F0 < E[St]: the long position expects compensation for the assumption of systemic risk! 30

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