1 / 20

Hedging, Insurance and Diversifying

Chapter Eleven. Hedging, Insurance and Diversifying. Chapter Outline. Using Forwards And Futures Hedging Foreign Exchange Risk With SWAP A comparison : Insurance VS Hedging & no action Diversification Principle (Portfolio Theory) Computing –Correlation Coefficient

akina
Download Presentation

Hedging, Insurance and Diversifying

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter Eleven Hedging, Insurance and Diversifying

  2. Chapter Outline • Using Forwards And Futures • Hedging Foreign Exchange Risk With SWAP • A comparison : Insurance VS Hedging & no action • Diversification Principle (Portfolio Theory) • Computing –Correlation Coefficient • The Perfekt Diversification • An Alternative Calculation of Portfolio Variance

  3. Using Forwards And Futures • Forwards • A contract between any two person, obligates one to sell and the other to buy an assetin the futureat a fixed P( FORWARD Prices, F). • Price of immediate delivery (called Spot price, Pt) • No money is paid now by either party. • The face value of the contract ( Q * F) • The buyer is said to take long position • The Seller is said to take short position • Forwards reduce risks for both buyers and sellers. • Futures (more liquid) • Standardized (quantity and quality)- • Traded in organized exchange • Sellers and buyers has separate contract (with future exchange market not with each other).

  4. Example - Futures • A farmer wants to sell wheat (Q = 100 000k) . F = $2K Face value = $200 000…..in one month time. • Three transactions : • 1- Sign standardized Futures contract with future exchange (Q = 100 000k at F =$2 per k) at time (t). • 2- In a month time, the farmer sell to his own distributor and the buyer gets wheat from his supplier at the Pt+1 • 3- Each party pays (gets) the difference from the stock Exch. • Assume (Pt+1=$1.5) • Stage 2 the farmer gets ($1.5x 100 000=150 000) • Stage 3 the farmer gets( 50 000) • The opposite for the buyer

  5. Hedging Foreign Exchange Risk With SWAP Contracts • Swap; 2 parties exchanging (Swapping) a series of cash flows at specific interval over specific period. It is a series of Future. • No immediate payment: goods, currencies and securities or interest rate. • counterparty • Ex. A Swedish exporter will get $100 000 a year over the next 10 years from a Chinese Company. You want to eliminate exchange rate risk. Assume: Et = F = 10 k/$. • Stage (1): You enter a currency swap now (time t) exchange $ with SEK (national amount) • Stage (2): Assume Et+1= SEK 9/$1 • The exporter recive : $100 000 (9) = 900 000SEK • Stage (3): the exporter gets 100 000 SEK from stock Exchange

  6. A comparison : Insurance VS Hedging & no action • 1-Future: The Farmer can Sell using Future . F = $2 . Short position • 2-insurance: to grantee a min Pt+1 of $2. Premium = $20000. • if Pt+1 > $ • if Pt+1< $2. use the insurance (gets $180 000). • 3-No action. • If he knows for sure Pt+1 $400 $300 $200 $100 $0 No Action Insurance Hedging $0 $1.5 $2.0 $3.0 $4.0

  7. Diversification Principle (Portfolio Theory) • Diversify: splitting an investment among many risky assets • Diversification Principle; Diversification can sometimesrisk exposure without E( R). • Uncorrelated assets and the right weight • EX. You have $100 000. Two stocks. For each asset if succeed = 4 times and if fail = 0. Probability 0.5(succeed) and 0.5(fail ). The current price is $1 per share • Expected Return & Variance if you by Either (A) or (B) • (1) • E (R ) = .5(0) + .5($400 000) = $ 200 000 • (2) • = 0.5(0-200 000)2+ 0.5(400 000 –200 000)2 = 40 000 000 000 • σ = √40 000 000 000 = 200 000(3)

  8. Diversification Principle (Portfolio Theory) • Expected Return & Variance if a Portfolio (50% ----50%) • E( R)P = w A(E(R)A) +w B ( E (R )B) + w C (E(R)C) + (4) • E ( R)P = 0.5 (200 000) + 0.5(200 000) = 200 000 same • Variance if we know correlation( ρ): • (5) • (6) • Assume(ρ=0), usingequation(5) : • (0.5)2 (40 000 000 000)2+(0.5)2 (40000000000)2 =20000000000 • Then, σ=√20 000 000 000 = 141 421

  9. Correlation • So far, we assumed that assets were uncorrelated. • In practice, assets are highly correlated ( rec. and boom) • This limit the success of diversification • When mixing 2-risky assets, correlation & the weights will determine the SD of the portfolio.

  10. Example- Singel Asset or a portfolio • You have $100 000 to invest. Two stocks ( SAAB and VOLVO). You are indifferent of whether to : • buy only 1 stock, which? Or • invest in a portfolio of two? • You are given the flowing:

  11. Example- Singel Asset or a portfolio • Case (1) : if you invested the $100 000 on only one stock. Which one you have to choose? • We know that

  12. Example- Singel Asset or a portfolio • Case (2): What happens if we combine both? Portfolio • Put $50 000 on SAAB and $50 000 on Volvo. • Assume ρ=-1. • E( R)P = w1(E(R)1) +w2 ( E (R )2) + …. • = 0.5 (.14) +.5(.02) = 8% Regardless business cycle • = (0.5)2 (0.04) + (0.5)2 (0.04) + 2 (0.5)(0.5) (-1) (0.20)(0.20) • = 0.25 (0.04) + 0.25(0.04) – 0.02 = 0.02 -0.02 = 0 • = 0 • All risk is eliminated because (1) A NEGATIVE PERFECT CORRELATION (-1), and (2) Optimal weight

  13. Computing –Correlation Coefficient • How to Calculate Correlation Coefficient? • Two steps: • Calculate the Covariance between two stocks: • = -1 (.20)(.20)=-0.04 (1) • Calculate the Correlation Coefficient (  rho): • = -04/(0.20)(0.20)= -1 (2) • IF we don’t know the Covariance. Apply : • (3) • = 1/3(.385-0.14)(-.225-0.02) + 1/3(.140-0.14)(0.02-0.020) + 1/3(-.105-.14)(.265-0.02) = - 0.04 • Asset A=SAAB, Asset B (VOLVO). (1): Strong, (2) normal, 3(weak)

  14. The Perfekt Diversification • 1- Negative Correlation (ideal -1) • Assume two stocks (A och B) with : • σ A = 4 σ B = 3 and youInvest 50% on each. Calculate the risk in such portfolio. • If ρ = +1: • If ρ = +0.5: • If ρ = 0: • If ρ = -1:

  15. The Perfekt Diversification • 2- Choose the Optimal Weights : • If two stocks : the optimal weight for stock (A): • That is: • The optimal weight is 0.4 286 for (a) and the rest (0.5714) for stock (B) • Try Now: • = (0.4286)2(4)2+(0.5714)2(3)2+2(0.4286)(0.5714)(-1)(4)(3) = 0

  16. Example: Portfolio Weights • Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? • $2000 of DCLK • $3000 of KO • $4000 of INTC • $6000 of KEI • DCLK: 2/15 = .133 • KO: 3/15 = .2 • INTC: 4/15 = .267 • KEI: 6/15 = .4

  17. An Alternative Calculation of Portfolio Variance • Compute the expected return for each single stock under each state of the economy. • IF Two states (1(boom) & 2(recessio)) & 2 stocks (A &B) • E(R)A= Pr.1(R1) + Pr.2( R2) • E(R)B= Pr.1(R1) + Pr.2( R2) • Compute the expected portfolio return using: • E(R)P = w A (E(R)A+ w B (E(R)B • Compute the portfolio return for each state: • RP 1 = wARA + wBRB + boom • RP 2 = wARA + wBRB + … recession • Compute the portfolio variance and standard deviation

  18. An Alternative Calculation of Portfolio Variance Three stocks with the following • Calculate portfolio Expected Returns and the variances if you invest 50% of your money on stock (A), 25% on stock (b) and 25% on stock (C ). • E(R) for each individual stock under two states: • E(R)A= Pr.1(R1) + Pr.2( R2) = .40(.10) + .60(.08) = 8.8% • E(R)B= Pr.1(R1) + Pr.2( R2) = .40(.15) + .60(.04) = 8.4% • E(R)C= Pr.1(R1) + Pr.2( R2) = .40(.20) + .60(0) = 8 % • E(R)P if wA=50% w B=25% w C=25% • E(R)P = w A (E(R)A+ w B (E(R)B + w C (E(R)C • = .5(.088) + .25(.084) + .25( .08) = 0,044 + 0,021 + 0,02 = 8.5% • The Portfolio Return: • RP= 0.50 (.10)+ .25(.15) + .25(.20) = 13.75 % If BOOM • RP= 0.50 (.08)+ .25(.0.04) + .25(0) = 5% If Recession • σ2 = .40 (.1375-0.085)2 + .60 (0.05-0.085)2 = 0.0018375 σ =

  19. Example – Calculating a Portfolio’s Variance • Consider the following information • State Probability X Z • Boom .25 15% 10% • Normal .60 10% 9% • Recession .15 5% 10% • What is the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Y? if you have to choose only one of these two, which one you choose? • E(R) for each individual stock under 3 states: • E(R)X=.25(.15) + .60(.10) +.15(.05) = 0,105 • E(R)Z=.25(.10) + .60(.09) +.15(.10) = 0,094 • E(R)P if wX=60% w Z=40% • E(R)P = w X (E(R)X+ w Z (E(R)Z =.60(.105) + .40(.094)= 0,1006 • The Portfolio Return: • Portfolio return in Boom: .6(15) + .4(10) = 13% • Portfolio return in Normal: .6(10) + .4(9) = 9.6% • Portfolio return in Recession: .6(5) + .4(10) = 7% • σ2P= .25(13-10.06)2 +.6(9.6-10.06)2 + .15(7-10.06)2 = 3.6924 & σ P = 1.92%

  20. Example-Calculating Return-to-risk ratio • Calculation the variance for a single asset • Comparison between X and z

More Related