程序代写 AREC3005 Agricultural Finance & Risk

Topic 7: Diversification and hedging
Shauna Phillips
School of Economics

AREC3005 Agricultural Finance & Risk
, file photo: Reuters, file photo
Dr Shauna Phillips (Unit Coordinator) Phone: 93517892
R479 Merewether Building

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Introduction
› For the most part, we are discussing techniques for handling loss exposures related to speculative risks
› Two common approaches to handling speculative risk are: – Diversification
› Risk-diversification applies risk-reduction concepts from portfolio theory
› Hedging can be used to reduce vulnerability to a variety of financial risk exposures

Risk-bearing financial institutions
› Risks that could potentially ruin an individual or small firm are less likely to devastate a larger firm, especially if it doesn’t experience losses from several exposures simultaneously
› Large firms can usually bear risk in a more cost-efficient manner e.g. by hiring advisors, and being better informed about risks
› Most importantly, risk is reduced by combining individual exposure units into a group and sharing the average loss experience for the group across all group members
– An example is insurance companies reducing their policyholders’ exposure to pure risk through the use of risk pooling

Covariance and correlation
› To understand risk reduction through diversification, we need to understand how the risk exposure of one group member is related to the risks of all other group members
› We need to know something about: – Expected value
– Standard deviation/Variance
– Covariance
– Correlation coefficient

Covariance and correlation
› The following example is taken from Dorfman and Cather (2013, Ch. 5) › A common example of risk diversification using an investment portfolio
– A common practice is to purchase stocks/shares based on their forecasted return (following some kind of analysis)
– Consider a simple example with only 2 stocks and 2 states of the economy (i.e. states of nature)

Covariance and correlation
› Naturally, an investor is concerned with the expected value of the returns of the stocks
› However, equally important is whether the returns of the two stocks are interrelated
– Do the returns move in the same direction? – Do the returns move in opposite directions?
› The direction of the interrelationship is measured by the covariance of the returns

Covariance and correlation
› A three-step process is used to calculate the covariance of the returns
Calculate the expected return from each stock , E(Ri) =ΣP(Ri)* Ri Subtract the expected return from the actual return, Ri -E(Ri), for each
state of nature.
For each state of nature, multiply:
i. ii. iii.
Probability of the state of nature occurring
Difference between expected and actual return for Stock A
Difference between expected and actual return for Stock B …and sum these products across all states of nature.

Covariance and correlation (Table 1)
State of Economy
Returns: RA
Returns: RB
RA – E(RA)
RB – E(RB)
Col 2 × Col 5 × Col 6
• Expected return for Stock A = 0.5×22 + 0.5×10 = 16%
• Standard deviation of returns for Stock A =
[0.5×(22 – 16)2 + 0.5×(10 – 16)2]0.5 = 6%
• Expected return for Stock B = 0.5×14 + 0.5×2 = 8%
• Standard deviation of returns for Stock B =
[0.5×(14 – 8)2 + 0.5×(2 – 8)2]0.5 = 6%

Covariance and correlation
› A three-step process is used to calculate the covariance of the returns
Calculate the expected return from each stock (16% and 8%)
Subtract the expected return, E(Ri), from the actual return, Ri, for each state of nature (Columns 5 and 6)
For each state of nature, multiply:
Probability of the state of nature occurring (Column 2)
Difference between expected and actual return for Stock A (Column 5)
Difference between expected and actual return for Stock B (Column 6) …and sum these products across all states of nature
i. ii. iii.

Covariance and correlation
› The covariance measures how two random variables (e.g. returns of two stocks, insured losses of two shops) co-vary, or move relative to each other
– Positive covariance means the variables move in the same direction – Negative covariance means the variables move in opposite directions
› In our example, both stocks have above-average returns when the economy is strong and below-average returns when the economy is weak
– Positive covariance

Covariance and correlation

Negative correlation (Table 2-1)
State of Economy
Returns: RC
Returns: RD
• Expected return for Stock C = 0.5×10 + 0.5×30 = 20%
• Standard deviation of returns for Stock C = [0.5×(10 – 20)2 + 0.5×(30 – 20)2]0.5 = 10%
• Expected return for Stock D = 0.5×40 + 0.5×0 = 20%
• Standard deviation of returns for Stock D = [0.5×(40 – 20)2 + 0.5×(0 – 20)2]0.5 = 20%

State of Econom y
Recessio n
Returns: RC
Negative correlation (Table 2-2)
Returns: RD
RC – E(RC)
RD – E(RD)
Covarianc es

Zero correlation (Table 3-1)
State of Economy
Returns: RE
Returns: RF
Status quo
• Expected return for Stock E = 1/3×15 + 1/3×11 + 1/3×10 = 12%
• Standard deviation of returns for Stock E =
[1/3×(15 – 12)2 + 1/3×(11 – 12)2 + 1/3×(10 – 12)2]0.5 = 2.16%
• Expected return for Stock F = 1/3×9 + 1/3×3 + 1/3×12 = 8%
• Standard deviation of returns for Stock F =
[1/3×(9 – 8)2 + 1/3×(3 – 8)2 + 1/3×(12 – 8)2]0.5 = 3.74%

State of Econom y
Status quo
Recessio n
Returns: RE
Returns: RF
Zero correlation (Table 3-2)
RE – E(RE)
RF – E(RF)
Covarianc es

Risk diversification

Negative correlation (Table 2-1)
State of Economy
Returns: RC
Returns: RD
• Expected return for Stock C = 0.5×10 + 0.5×30 = 20%
• Standard deviation of returns for Stock C =
[0.5×(10 – 20)2 + 0.5×(30 – 20)2]0.5 = 10%
• Expected return for Stock D = 0.5×40 + 0.5×0 = 20%
• Standard deviation of returns for Stock D =
[0.5×(40 – 20)2 + 0.5×(0 – 20)2]0.5 = 20%

Risk diversification in negatively correlated groups

Risk diversification in positively correlated groups

Risk diversification in positively correlated groups
› A mutual fund is an investment fund that collects investment capital from a large group of investors and invests it in a well-diversified pool of investments (in equity funds, bond funds, etc.)
– A small investor can invest say $100 and have it spread over fractions of shares in many different stocks and bonds
– Mutual funds take advantage of lower transaction costs
– Research and brokerage costs are spread over many investors, rather than each
investor bearing the cost of their own research and paying their own brokerage
– However, most stock prices are positively correlated over time, moving in response to the same market-wide factors (e.g. interest rates, economic growth)
– These price-change risks are systematic (i.e. undiversifiable risks)
– Q: What, then, is the major advantage of investing in a mutual fund (especially,
for small investors)?
– A: These funds can diversify away the negative consequences of firm-specific risk (i.e. idiosyncratic or diversifiable risks)
– e.g. poor strategic decisions, unsuccessful product launches, lawsuits, etc.

Risk diversification in uncorrelated groups: Insurance risk

Risk pooling with more than two exposure units

Risk pooling with more than two exposure units
› Combining independent, thus uncorrelated, exposure units in a risk pool results in a significant reduction in risk, even with relatively modest pool sizes
– Why? Because the standard deviation of the risk pool varies inversely with the square root of the number of independent exposure units in the pool
Standard deviation in risk pool
Size of Pool
Independent

Risk pooling with more than two exposure units
› In practice, the exposure units are likely to be positively correlated to some degree
– Many businesses in the same area being susceptible to road congestion, zoning changes, population change, etc.
– Many homeowners being susceptible to the same extreme weather events at the same time e.g. floods, earthquakes, hail
As we already know, pooling across non-perfectly positively correlated units will reduce risk, but not as effectively as pooling across uncorrelated units
Standard deviation in risk pool
Size of Pool
Independent
Correlation = 0.1

Risk pooling with more than two exposure units

Hedging of speculative financial risk
› Hedging is taking two financial positions simultaneously whose gains and losses will offset each other for the purpose of limiting risk
– Farmers can hedge by trading in both the spot and futures markets
– We can also view insurance as a hedging of risk
– When an insured firm has a loss, it gains the right to collect insurance proceeds
› Many risks can be hedged, including: – Currency risk
– Interest rate risk
– Commodity price risk

Hedging of speculative financial risk
› Frequently, hedging relies on derivative securities
› A derivative security is a financial instrument whose value is derived from
the value of an underlying financial asset or commodity
– For example, a futures contract is an order placed by a trader in advance to buy or sell a commodity or financial asset at a later point in time, and at a specified price
– Risk managers can use futures contracts to provide a hedge when an increase or decrease in a commodity’s price can reduce profits
– Options- for a call option, gives the owner the right, (not the obligation) to buy some underlying instrument from the call writer or seller (price and date specified)-underlying instrument might be a futures contract.

Australian futures markets
› Traded on the Australian stock exchange: – Eastern Australian wheat
– WA wheat
– Eastern Australia feed barley
– Eastern Australia canola

Futures contracts
› Futures contract legally binding contract to deliver (sell or go short) (for an expected decline in price).
› OR a legally binding contract to take delivery (buy or go long) (for an expected increase in price)
› Standardisation of quantity, quality, price, place & time of exchange.
› Hedgers and speculators take opposite positions. Hedgers shift the risk of adverse price movements. Hold an equal & opposite position in the cash & futures markets OR the substitute of a futures contract for a later cash market merchandising transaction.
› Futures markets work because of differences in opinion about the market.

Forwards contracts V futures
Forward contract
Futures contract
Unique agreement between 2 parties
Parties liaise through brokers and futures exchange
Non-standardised contracts
Standardised contracts
Exposed to “performance” risk
No “performance” risk
Negotiation expenses
No negotiation expense
Markets not liquid
Liquid markets
Relatively high transactions costs
Relatively low transactions costs

No physical delivery
› Seller of a futures contract makes a commitment to deliver a quantity of a defined grade of the commodity at particular date.
› The buyer makes commitment to take delivery of that amount.
› In practice no physical exchange occurs. Deliveries aren’t made, traders make offsetting transactions in the futures market before delivery date- if an operator buys a contract for wheat for delivery in January, then sell prior to January- this voids original obligation.
› The farmer sells futures, and closes out by buying back a futures contract, effectively cancelling it around the time the commodity is sold on the market.

› Prices in spot (cash) markets for commodities and prices in futures markets for the same commodities.
› Cash price-futures price = basis.
› Basis can be positive or negative (usually < 0 ) (reflects transport + storage costs). If spot market price is 5c above (below) futures price, the basis is described as 5 over (under). › Basis usually < 0 around harvest time (might be > 0 if stocks are low).
› Basis narrows as delivery date nears-cash and futures prices converge
-this narrowing reflects the decreasing cost of storage as delivery time approaches.

Futures and spot market prices (source: IMF(2004)

Price convergence
› Suppose the price of a cotton futures contract is $10, spot price of cotton $6 and a cost of delivery of $1.
– Profitable to purchase cotton in spot market for $6 and sell a futures contract for $10.
– Cash market cotton purchased for $6 can be stored & delivered for $1. – On delivery date, price of $10 received (profit of $3 cents per unit).
› Arbitrageurs respond to the profits- buying pressure in the spot market and selling pressure in the futures market) – ultimately spot market and futures market prices converge.

Hedging of speculative financial risk
› Consider an airline that must buy jet fuel in large amounts each month, as well as the oil refiner that will sell the fuel
› It is currently March and oil sells for $50 per barrel [this is the cash or spot price]
– Both companies are profitable at this price level
– If the price increases (to, say, $60), the airline is worse off and the refiner is better off, and vice versa

Hedging of speculative financial risk

Hedging of speculative financial risk
› If the spot price in November turns out to be less than $51, the airline will make a loss in the futures market (because the futures and spot prices will converge), and an offsetting gain in the spot market (because the airline can more cheaply purchase the oil on the spot market, instead of through the futures market)
› If the spot price in November turns out to be greater than $51, the airline will make a gain in the futures market (because the futures and spot prices will converge), and an offsetting loss in the spot market (because the airline can more cheaply purchase the oil through the futures market, instead of on the spot market)
› In both cases, the gains in one market are offset by losses in the other market
– All that is lost is the basis
– Regardless of what happens in the spot market between March and November, the airline has ‘locked in’ a price of $51

› Example: NSW farmer in May sowing wheat for November harvest – given price in May of November wheat futures & the expected November cash futures price relationship, the farmer can lock in a price for November.
› Framer calls broker and says sell November wheat at the market (go short) for a later cash market sale (November sell) – cash and futures markets prices move together.

Example: Hedging in wool markets (HHA2004)
› Aim in May –to protect price at which wool clip will be sold in future (September). Current cash price in May is $9.30/kg. Farmer needs $10.00/kg to cover costs. Basis is $0.70.
› In May, the farmer looks at futures price for September ; futures are trading at $10.00/kg so farmer fixes a price of $10.00 by going short (sell then buy back later).
› Come September, ready to sell and cash price has changed. Work through two examples:
– 20% price fall form $9.30 to $7.74
– 20% price rise form $9.30 to $11.16
– Either way farmer will sell wool in physical market and receive cash price, and close out the futures position.

Prices & transactions Price rises Price falls
May: Current cash price $9.30 /kg $9.30 /kg
Better example: wool producer
Futures price for October (sells a contract to deliver)
Current basis
September: Current cash price
$11.16 ( 20%)
$7.44( 20%)
Futures price for October
Current basis
Farmer’s transactions
May: sell October futures contract
September: sell wool at this price
Buy back October futures contract
Net price received

› Ultimately irrespective of whether the cash price rose or fell, the sheep farmer receives close to the futures contract price of $10.00/kg.
› So doesn’t lose from a price fall, but also doesn’t gain from a price rise.
› Wool processing companies may wish to operate to avoid price rises in wool markets. They would take out futures contracts to buy – opposite position to the farmer in the example above.
› Of course there are transactions costs associated with futures market operations. Hedging is attractive if the futures price exceeds the farmers expected cash price value by a margin that covers these costs.
› Another possibility available to the farmer to manage price risk is options trading. In agriculture most options have futures contracts as underlying assets.

Financial options
› Options are another type of derivative (similar to a future), where the option holder has the right, but not the obligation, to buy or sell a commodity or financial asset at an agreed-upon price for a specific period
– The option holder has the long position, which gives them the right to buy or sell under the agreed terms
– The option writer has the short position, and is obligated to buy or sell, based on the choice of the option holder
› European options V American options

› Long call option:
– The right, but not the obligation, to buy a commodity or financial asset
– Will exercise the option if the exercise/strike price is lower than the spot price
– Will allow the option to expire if the exercise/strike price is higher than the spot price
› Long put option:
– The right, but not the obligation, to sell a commodity or financial asset
– Will exercise the option if the exercise/strike price is higher than the spot price
– Will allow the option to expire if the exercise/strike price is lower than the spot price
› Short call option:
– Will be obligated to sell a commodity or financial asset if the option holder (long position)
exercises the option › Short put option:
– Will be obligated to buy a commodity or financial asset if the option holder (long position) exercises the option

› If a call owner decides to exercise their call owner declares the right to buy a futures contract, the brokerage firm is notified and it submits an exercise notice to the futures exchange where the option is traded.
› The clearing corporation at the exchange randomly chooses a brokerage firm with a short call position (matching the long call being exercised).
› Brokerage firm then randomly chooses a customer with a short call position and issues an assignment notice.
› Ultimately, the call owner is the buys the futures contract, from the call writer (seller).
› Price? Called the strike price of

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