Derivatives for dummies - Currency Forwards

The valuation of currency forwards are based on some of the very basic principles of Macroeconomics.

Interest rate parity:- According to the Interest rate parity principle, suppose you invest in your home country and earn a return, this return has to be equal to the return you achieve by borrowing a foreign currency and investing in that country and then converting it back to your home currency. To understand this better let us consider a small example.

Suppose you are an NRI and you live in US, the interest rate in India is 10% and the interest rate in US is say 5%. Superficially it might look that there is this great investment opportunity in India. Borrow in US at 5% and invest in India. Doing so earn 10% in India, pay back 5% as interest and hence make a clear riskless profit of 5%. But to our dismay this isn’t the case. Interest rate parity says that you will earn the same 5% return if you are a US investor. To understand this let us extend this example.

Suppose you are sitting in US having $1million to invest. You decide to invest this sum in India which is “An emerging market”. The current exchange rate is INR 45/$. Therefore you invest a total of 1million*45= 45 million Indian rupees in India. After a year at 10% you earn a handsome 10%*45 million= 4.5 million. As you are a US investor you want your returns to be in US$, so you convert the Indian rupee returns to $. Now the question is what will be the exchange rate one year from now. This is where INTEREST RATE PARITY comes into play. It says that there is no incentive of remaining unhedged in foreign currency. In other words you will get a return of only 5% that is the return you will get by investing in US markets. This can only be because of currency rate movements. Here are two golden principles to remember

·         The country whose return is higher in nominal terms with respect to another country’s return, currency will depreciate for that country with respect to the other country.

·         The country whose return is lower in nominal terms with respect to another country’s return, currency will appreciate for that country with respect to the other country.

In our example as we have seen that the Indian nominal rate of return (10%) is higher than that of US (5%). Therefore the Indian rupee will depreciate and the US $ will appreciate so that the return in both the currencies is same. Going back to the example, the US investor has 45+4.5 million INR. And we know that he gets only 5% return in US $ terms or 1.05 million US dollars, the exchange rate after 1 year has to be 49.5/1.05= 47.14INR/$ or the rupee has depreciated and the $ appreciated. To make it more generalized

Expected spot rate after t years = S_o * (1+R_dc)^T/(1+R_fc)^T

Where

 S_o= Current (spot) exchange rate domestic currency in foreign currency terms. (ex 45/$ is S_o for an Indian investor.

R_dc= Interest rate in domestic market.

R_fc= Interest rate in foreign market.

As forward rate is an unbiased predictor of Expected spot rate. Forward rate = Expected spot rate.

In the next issue we will see how the forward contracts are priced before expiry.

Shubham Goel

IIM Rohtak

Continue Reading - Derivatives for dummies - Currency Forwards

Derivatives for dummies: Hedging strategies using forward contracts

An important question that the investors face is how to protect their portfolio in times of volatility. One way is getting out of the cash markets (stock market) for now and entering again when market stabilizes. But this strategy may lead to a lot of uncertainty about the price that the investors will have to pay to enter again. To hedge this uncertainty and lock in the futures price the investor can make use of the derivatives products. In this article we will be talking mainly about how to hedge a portfolio by using futures and forward contracts (as both are almost similar in nature).

To learn this strategy one must know a very important   concept of beta (β).

Beta is the relative movement of the stock with respect to market. Suppose Nifty moves 1 point up the stock of the company with a beta of 1.2 will move 1.2 points up. Beta is actually the systematic risk measure of the company. Actual in depth discussion will be done in subsequent articles.

β = covariance (stock index, stock)/variance of the stock

This may sound too mathematical for the common investor so in simple words to find the β of a stock an investor can Google to find the β of a stock or use a simple excel tool to find out the same. What the investor would need is the historical weekly closing price of the stock for two years and the weekly closing price of NIFTY for two years. Our website want2rich.com will soon have the same. After you have the data, put the data of the stock in column A and data of NIFTY in column B. Use the function =slope(range of stock, range of NIFTY). The value is the β of the stock. To calculate the β of the whole portfolio use the following formula

Beta of the portfolio = weighted average of betas of individual stocks=∑ βi*wi

Where wi= market value of investment in stock i/ market value of the whole portfolio.

The strategy

Suppose a manager has a portfolio consisting of three securities of Rs20 lakh, with a beta value of 1.17. The investor speculating turmoil in near future wants to reduce the beta of the portfolio to:

·         0 or no matter how the markets move investor will not incur a loss.

(a) To decrease the portfolio beta from 1.17 to 0, the portfolio manager may sell off a portion of equities and use the proceeds to buy risk free securities.

If we designate the existing portfolio as asset 1 and the risk free security as asset 2, we have,

β_p =w₁β₁ + w₂β₂= w₁β₁ + (1-w₁) β₂

(Since the new portfolio consists of only two assets), we have β_p = 0, β₁ = 1.17, and β₂ = 0(this being a risk free asset).

Substituting the known values, we get

0 = w₁ x1.17 + (1- w₁)0

Or, w₁ = 0

Or the investor will have to sell of the whole portfolio and invest in risk free securities like govt. bonds.

(b) Alternatively, the manager can sell stock index futures contracts. Rupee value of the spot position to be hedged = 20 lakh .The amount of future contract of NIFTY to be sold= 1.17 x 20 lakh =Rs 23.4 lakh.

This way whatever will be the loss in the cash portfolio it will be offset by the forward/ future contract. Let us see how

Suppose the market (NIFTY) dips by 10%. The loss in the cash market portfolio will be equal to 20lakh*10%*1.17(β)= 2.34 lakhs. By shorting the NIFTY contracts the profit investor will make here = 23.4 lakh * 10%= 2.34 lakhs. Total loss = 2.34 lakhs- 2.34 lakhs=0.

Thus we can clearly see that by using derivatives instrument you can hedge your portfolio without exiting the cash market. The investor can also reduce the β of the portfolio if he does not want to completely hedge his position. Let us extend our previous example and now suppose the investor wants to reduce the β of the portfolio to .9 from an initial 1.17.

•          (a) To decrease the portfolio beta from 1.17 to 0.9, the portfolio manager may sell off a portion of equities and use the proceeds to buy risk free securities. Using the same formula              β_p =w₁β₁ + w₂β₂= w₁β₁ + (1-w₁) β₂

We have β_p = 0.9, β₁ = 1.17, and β₂ = 0(this being a risk free asset). Substituting the known values, we get             0.9 = w₁ x1.17 + (1- w₁) 0 , Or, w₁ = 0.76923 or the investor will have to sell of (1-.76923)*20 lakh= Rs4.6154 lakh of equities and invest in govt. bonds.

(b) OR rupee value of the spot position to be hedged = Rs4.6154 lakh (1-.76923)*20 lakh.The amount of future contract to be sold= 1.17 x Rs4.6154 lakh =Rs 5.4 lakh. Investor has sold future for Rs5.4 lakh .If future price reduce by 10% because of general decline of market of 10%, he will earn from future selling = Rs 5,40,000x.1 = Rs 54,000. Now, since they are holding the same portfolio having β=1.17, portfolio value will reduce by 11.7% for a 10% decline of market price.Thus portfolio reduces by Rs20 lakh x(.117)=Rs2,34,000.                                                            Less: Earning from future selling   =   54,000. Total loss = Rs1,80,000  (loss of 9% when market falls by 10%)  or a β of 0.9.

Shubham Goel
IIM Rohtak

Continue Reading - Derivatives for dummies: Hedging strategies using forward contracts

Derivatives for Dummies II

FORWARD MARKETS AND CONTRACTS

FORWARD CONTRACTS

A forward contract is a contract between two parties in which one party agrees to buy and one party agrees to sell a particular asset at a particular date in future. Suppose today is June 13^th and the two parties go into a contract, one party agrees to buy 1000 quintals of wheat at INR. 2000/ quintal on August 30^th and one party agree to sell. The buying party is said to be LONG the forward contract and the selling party is said to be SHORT the forward contract. At the initiation of the contract there is no exchange of money. If the price of the asset increases over the time period before the expiration of the contract the long party wins otherwise the short wins. Considering the same example, suppose on July 10^th the price of wheat becomes INR.2500 in the cash market. The long party wins because it has the right to buy a quintal of wheat at INR 2000 where as the current price for buying the same quintal of wheat is INR 2500. So the long party makes a profit of clean INR 500/ quintal or a total of 500*1000= INR 500000 and the short party makes a loss of the same amount. If the future price of the asset falls below the contract price( say INR 1500/ quintal), the result is opposite and the short party which has the right to sell at an above-market price( INR 2000/ quintal) makes a profit of INR 500*1000= INR 500000 in this case . The forward contract can be thought of as a simple bet between two parties in which one party expects the price of the asset to go up and the other party expects the price of the asset to go down.

More often FORWARD contracts are used by large companies to hedge their risk of buying or selling at a price which is uncertain. They want to lock in the price and reduce the risk (uncertainty). The other parties involved are speculators who want to earn profit on changes in prices and the arbitragers who earn when there are market inefficiencies.

Each party in a forward contract is exposed to default risk (or counterparty risk) as the forward contracts are over the counter contracts and are not backed by a clearing house. So there is a probability that the party which has lost the bet will not pay its obligations. This  risk  is absent in the case of futures contracts as these are highly standardized and are backed by a clearing house and both parties are required to deposit a margin money (typically 10% of the contract value).

Settlement Procedure:

Settlement can be done by:

·         Delivering the asset

·         Cash settlement

Consider the previous example in which the price of the quintal reaches INR 2500 on August 30^th. The long party has the incentive to buy wheat at below market price (in this case the contract price i.e. INR 2000/ quintal) and sell at the market price (INR 2500/ quintal).  This is one procedure for settling a forward contract at the settlement date or expiration date specified in the contract. An alternative settlement method is cash settlement. Under this method, the party that has a position with negative value is obligated to pay that amount to the other party. In the example, the short party can directly pay the difference between the contract price and the market price on the expiration date.  In this case (2500-2000)/quintal * 1000 quintals= INR 500000. Ignoring transactions costs, this method yields the same result as asset delivery. On the expiration (or settlement) date of the contract, the long receives a payment if the price of the asset is above the agreed-upon (forward) price; the short receives a payment if the price of the asset is below the contract price. It can be seen as a zero sum game and can be visualised as a simple bet on the prices, the winnings of which will be decided by the price of the asset under consideration.

How to Terminate a Position Prior to Expiration

A party to a forward contract can terminate the position prior to expiration by entering into an opposite forward contract with an expiration date equal to the time remaining on the original contract. Recall our example and assume that ten days after inception (June 23^rd), the short, expecting the price to go even higher on the termination date wants to terminate the contract. Since the short is obliged to sell the asset only on August 30^th it can effectively terminate the contract by entering in a long contract with the same expiration date as the short contract of the original forward contract i.e. entering into a forward agreement with expiration date August 30^th and date of inception of contract June 23^rd with a contract price of say INR 2200/ quintal. The position of the original short now is two-fold, an obligation to sell wheat at INR 2000/ quintal and an obligation to buy wheat at INR 2200/quintal. Thus he locks in a loss of INR 200/quintal*1000quintals=INR. After that he is effectively out of the Forward contract or has terminated the contract regardless of the market price of wheat at the settlement date. No matter what the price of a quintal of wheat 2 months from now, he has the contractual right and obligation to buy a thousand quintals at INR 2200/ quintal and an obligation to sell at INR 2000/quintal. However, if the short's new forward contract is with a different party than the first forward contract, some credit risk remains as the other party may not pay up the profit. An alternative is to enter into the second (offsetting) contract with the same party as the original contract. This would avoid credit risk since the short party can pay only the difference to the long party.

There are different types of forward rate contracts with various asset classes as their underlying. We will review each one separately including the pricing of each in the coming article. Just to give you an idea below is the list of different asset classes on which forward agreements are customised:

·         Equity Indexes

·         Zero coupon bonds

·         Coupon bonds

·         Floating rate bonds (LIBOR, EURIBOR, MIBOR)

·         Currency exchange rates

Shubham Goel

IIM Rohtak

Continue Reading - Derivatives for Dummies II