A bond is a term debt security that certifies the loan relationship between its owner and the issuer. Bonds can be issued by the state represented by national authorities, local authorities, joint stock companies, and private enterprises. The issuer must make all payments on bonds in the first place in comparison with shares and on a mandatory basis.
Payments are secured by the property of the issuer. A bond is a term paper. As a rule, the issuer redeems it at par. Bonds can be issued subject to early withdrawal or redemption. Bond with the right early repayment allows the investor to present it to the issuer ahead of schedule for redemption. These bonds usually cost more when placed, as the risk is borne by the issuer.
A classic bond is a security that pays a fixed income. The yield on a bond is called interest or coupon. The bond itself is called a coupon or hard-interest paper. In the context of inflation, the face value of the security is also subject to devaluation. Therefore, there are indexed bonds. Not only the coupon is floating, but the face value is also indexed.
There are zero-coupon bonds. A zero-coupon bond is a security that has no coupons. The investor's income arises from the difference between the bond's redemption price (par) and the purchase price. Zero-coupon bonds are also attractive for an investor if he needs to accumulate a certain amount of money by a certain time. Having bought the required number of bonds, the depositor no longer depends on the conjuncture, as is the case with a coupon security.
The next type of bond is the convertible bond. In accordance with the terms of the issue, it can be exchanged for shares or other bonds.
The bond has a par, which is paid when the security is redeemed. If the bond is not zero-coupon, then its yield is specified as a coupon. The coupon represents a certain percentage.
Depending on the market situation, a coupon bond can be sold at a price either below or above par. The difference between the face value of a bond and the price, if it is lower than the face value, is called a discount or discount, or de-zagio. The difference between the price of a bond, if it is higher than par. and the face value is called a premium or premium.
It is customary to give bond quotes as a percentage. In this case, the face value of the paper is taken as 100%. To find out the price of a bond in rubles from a quotation, multiply the quotation as a percentage by the face value of the bond.
Depending on the state of the market, the price of a coupon bond may be higher or lower than par. However, by the time of its redemption, it must necessarily be equal to the face value, since the security is redeemed at face value. The bond price can be divided into two parts: the net price and the accumulated coupon amount.
It is advisable to make such a division in order to better represent the dynamics of the bond market value. During the coupon period, it is equal to the sum of the net price and the amount of the coupon accumulated at the time of the transaction. On the coupon payment date, it falls by the coupon size.
Determination of the market value of securities is based on the principle of discounting. An investor purchases a security in order to receive the income that it brings. Therefore, in order to answer the question of how much this or that security should cost today, it is necessary to determine the discounted value of all income that it will bring.
The technique for determining the market value can be represented in three steps:
1. Determine the income stream that is expected for the security.
2. Find the discounted value of the value of each payment on the security.
3. Let's summarize the discounted values. This amount is the market value of the security.
The most important point in calculating the price of a bond is to determine the discount rate. It should correspond to the level of investment risk. The discount rate can be represented as follows: the risk-free rate can account for inflation. By purchasing securities, the investor faces the liquidity risk associated with that. how quickly and at what price the paper can be sold. Therefore, this value should be reflected in the discount rate.
Determination of the market value of bonds allows the investor to calculate the level of the security price that is acceptable to him. At the same time, this does not mean that bonds on the market will necessarily be sold at the found price. In addition, the forces of supply and demand will also affect the price. If demand exceeds supply, then this will create a potential for an increase in prices, if supply is greater than demand, then for a decrease.
When designing a bonded loan, the company calculates the parameters of bonds (issue volume, coupon rate, circulation period, etc.), and also calculates the price at which bonds can be sold on the market. Investors, in turn, evaluate the parameters of the issue and determine the price at which they are ready to purchase these bonds. The issue of bonds will take place only if the interests of the company and investors coincide with the price of the bonds.
An investor, purchasing a bond, expects to receive periodic coupon payments, but on the expiration of the bond's validity, he expects to receive its par value. In this case, the buyer of the bond proceeds from the fact that coupon payments will bring him a certain rate of return on invested capital. However, these payments (coupon payments and redemption at par) will occur in the future, and the bond must be purchased today. Therefore, it is necessary to assess the future cash receipts on bonds.
Bond price
In general terms, the current price of a bond can be represented as the value of the expected cash flow reduced to the current moment in time. Cash flow consists of coupon payments and the face value of the bond, paid at its redemption. Thus, the bond price is the present value of the coupon payments and the lump sum of the bond's par value at maturity.
The bond price is determined by the formula
where WITH - coupon payments; G - required yield; N is the par value of the bond; NS - the number of years to maturity of the bond.
If the company issues a three-year bond with a par value of 1000 rubles. with a coupon rate of 12%, at which coupon payments are made once a year and the market interest rate for similar bonds is 15% per annum, then the company can calculate the selling price of the bonds using the above formula
If the coupon yield is set at 12%, the company will not be able to sell the bonds at par. This is due to the fact that the market yield of similar financial instruments is 15% per annum, and the company will pay only 12% on coupons. Therefore, investors will not agree to purchase bonds at par, the company will have to reduce the price, and when it reaches the equilibrium level of 931.5 rubles. per bond, then a bond purchase and sale transaction will be made. If a company seeks to save on coupon payments (for example, set them at 8% per annum), then it will have to further reduce the selling price in order for investors to purchase bonds.
Coupon payments can be made several times during the year: quarterly or semi-annually (see Chapter 2). If payments are made several times a year, then the above formula is slightly modified and looks like this:
where T - the number of coupon payments during the year.
Consider the previous example of a three-year bond with the same parameters, but coupon payments are made twice a year. In this case, the bond price:
According to these bonds, the company will make six coupon payments for 60 rubles each during the period of their validity. each. As we can see, the price of a bond with semi-annual coupon payments is higher and amounts to 939.1 rubles. This is due to the fact that coupon payments are not made at the end of each year, but half-yearly. The investor earlier receives money that he can use for his needs. Therefore, for earlier arrivals Money he is willing to pay a higher amount for the bond.
Due to the fact that transactions with securities are carried out constantly, bonds are sold (bought) during the entire period of their circulation. The day of the transaction in most cases does not coincide with the beginning of the coupon period. The bond can be purchased on any day of the current coupon period. Therefore, when determining the price of the bond, it should be borne in mind that not an integer, but a fractional number of coupon periods remains until the maturity date, and the seller of the bond needs to reimburse the accumulated coupon yield. In this case, the price of the bond, for which the coupon yield is paid once a year, is determined by the formula
where WITH - the amount of coupon payments; G - yield to maturity (discount rate); NS - the number of years to maturity of the bond; i - serial number of the year from the current date; N is the par value of the bond; k- the share of the coupon period from the date of purchase of the bond to the date of its end;
where t - the number of days from the date of the transaction to the date of payment of the next coupon.
Example. Determine the price of a bond with a par value of 1000 rubles, at which a coupon yield of 10% is paid annually. Discount rate - 15%. The bond was purchased on the 60th day of the coupon period. 2 years and 305 days left until maturity.
Solution. To find the price of a bond, let's calculate the share of the coupon period from the date of purchase to the date of coupon payments:
Thus, the investor will receive the yield on the first coupon in 305 days from the date of purchase of the bond, which is 0.84 of the duration of the coupon period. The second coupon will be received in 1.84 years and the third in 2.84 years from the date of purchase.
In this case, the bond price can be calculated as follows:
If coupon payments are made several times during the year, then the above formula is slightly modified. Instead of the number of full years, it is necessary to take the number of coupon payments. In this case, the fractional part of the coupon period is determined taking into account the number of days in the coupon period. If the number of coupon payments per year T, then in the formula for determining the bond price indicators i and NS multiplied by T, and the magnitude k is determined by the formula
where t - the number of days from the date of the transaction to the date of the next coupon payments; T - the number of days in the coupon period.
When borrowing for a short period of time, enterprises sometimes resort to issuing zero-canon bonds, which are sold to investors at a discount but below par. A perkunless bond can be viewed as a special case of a coupon bond, only all coupons are zero. Therefore, the price of a zero-coupon bond is calculated using the formula
A distinctive feature of zero-coupon bonds, as mentioned above, is a short circulation period (up to a year). In this case n> which in the formula shows the number of years to maturity, is obtained as a fractional value. In order not to raise to a fractional power, in practice, a simplified formula for calculating the value of zero-coupon bonds is widely used:
where t - the number of days to maturity of the bond; G - market annual yield.
Example. Determine the price of a zero-coupon bond with a par value of 1000 rubles, which is issued by an enterprise with a circulation period of 182 days. The market interest rate for bonds of a similar type is 15% per annum. Under such conditions, the bond price
Unlike a stock, which is equity, a bond is a representative of borrowed capital.
Shares are issued only by joint-stock companies, bonds - by any and.
The purpose of the issue of both shares and bonds is to raise free capital in small portions, but from many owners on the terms of payment of a certain type of income. However, if for a share the issuer provides for the payment of its par value (or other monetary amount) only in the event of liquidation of the joint-stock company, then for the bond it is mandatory to pay its par value upon its redemption (redemption).
Differences between bonds and bank loans
A bond is a representative of borrowed capital, which is also a bank loan (credit). The difference between the bond form and the cash loan form is as follows:
- the bond constitutes only a single part of the capital loan required by the issuer, and not its entire volume;
- there is a bond loan agreement between the issuer and the ultimate lender, and the loan is taken from the bank, which itself attracts credit resources from the market;
- in the form of a bond, a loan can be traded on the market as a commodity, but a bank loan is not traded on the market.
Bonds can be issued in documentary and non-documentary forms. They can be registered and bearer.
Advantages of a bond over a stock
The owner of the bond, being a creditor in relation to, for example, a joint-stock company, has an advantage over shareholders: in the event of the liquidation of this company, his property rights are satisfied in the first place in comparison with the property rights of shareholders.
Restrictions on bond issuance
Joint Stock Companies have certain restrictions on the issue of their bonds, the main of which are that the par value of the issued bonds cannot exceed the size of the authorized capital of the company, which must be fully formed by the time the bonds are issued. In addition, if bonds are issued without collateral, then this is allowed only two years after the commencement of the operation of the organization.
Main types of bonds
By the type of issuer, bonds are divided into government and corporate. The former are issued by or on behalf of the state, and the latter are issued commercial organizations different types.
There are two main types of bonds:1.classic (unsecured)- such bonds give the owner the right to receive income, and the return of the invested amount is established at the time of placement.
Unsecured bonds do not have any collateral and are guaranteed by the overall high credit rating of the issuer and its image as a company fully meeting its market obligations;
2.provided, giving the same rights to the owners as classical, as well as the right to receive a part of the property of the issuer, which he offers as security.
V international practice there are two types of collateral: guaranteed and non-guaranteed.
Types of bond by lifetime: urgent and indefinite... The first ones are issued for a predetermined period of time, usually calculated in years, after which the bond's face value returns to its last owner. The second - without a specific maturity date, but which can be redeemed by their issuer under certain conditions. These conditions may, for example, consist in the right (option) of the issuer to determine the moment of redemption or in the right (option) of the owner of the bond (investor) to determine this moment. Other combinations of similar rights (options) are also possible.
Types of bond if possible exchange for other securities : convertible and inconvertible... The former includes the right, under certain conditions, to exchange for a certain number of other securities of a given company. The second have no such right.
Types of bond by the form of payment of interest income: coupon(percentage) and discount According to the first, income is paid in the form of a certain percentage of its face value, on the second, all possible income is determined as the difference between the face value of the bond and the price of its acquisition by the owner (the latter in this case is always less than the face value).
- Discount bond(zero coupon) - placed on the market at a price below par.
- Coupon bond(interest) - during the bond circulation period, interest is paid on it. Interest is called "coupon" because in the case where interest was paid several times, bonds were supplied with special coupons. When paying interest to the creditor, such a coupon was cut off with scissors and remained with the debtor as evidence of his fulfillment of his obligations.
For interest-bearing bonds, the amount of coupon payments can be constant or variable. The amount of payments on bonds with a variable coupon depends either on the intentions and capabilities of the borrower, or on some external factors.
Coupon interest and par value can be paid not only in money, but also in goods or property that have a monetary value.
Types of bonds by type of interest income: with constant, fixed, floating (variable) or depreciation income. The interest income on the first is known in advance (determined by the terms of the issue of this bond) and does not change during the entire period of its existence. For the second, the level of interest income is known in advance, but different in different coupon periods. On the third - the level of income changes according to the established rules during the circulation period of the bond. For the latter, the par of the bond is subject to return in parts, this is indicated during the placement, and coupon payments are paid to the remaining par of the bond.
The income paid on a bond is called interest, as opposed to a dividend, which is called income on a stock. It is set at a certain percentage of the bond's face value and can be, as already noted, either fixed (most often), or floating, changing over time.
Usually, a fixed interest income on a bond is paid every six months, in contrast to a stock, for which the most commonly used dividend payment period (in world practice) is every three months (otherwise it would be very difficult for the market to predict the dividend level for a longer period) ...
Theoretical bond price
The formula for the theoretical price of a bond takes into account all the interest income received on it for the entire period of its circulation and the return of the bond's par value, but in the form reduced to the current moment of time:
C about = ∑ (P i / (1 + r) i) + N / (1 + r) n, (2.6)
- About- theoretical price of a bond at a given time;
- Pi- interest income on the bond, paid in the i-th period;
- N- the face value of the bond returned at the end of its circulation period in the n-th period (year);
- r- risk-free interest rate of return.
For bonds with fixed income, interest income on which is paid in the same amount every year (period), general formula prices can be simplified:
C about = P / r (1 - 1 / (1 + r) n) + N / (1 + r) n , (2.7)
where P is the fixed interest income paid on the bond in each period (year) (P i = P).
This formula can be simplified even if n is the number of periods of income payment, or otherwise - the number of years of bond circulation increases significantly, for example, up to 50-100 years. In this case, the second term tends to zero, and in the first, the expression in parentheses tends to unity. As a result, we get
C about = P / r. (2.8)
It is easy to see that this formula is identical to Formula 2.2, that is, with long circulation periods and with the same annual income (dividend, interest), the price of a share is theoretically no different from the pricing of a bond, and only temporary differences (differences in circulation times) and the unstable nature of the dividend paid on ordinary shares make differences in the process of their prices formation.
In practice, to calculate the theoretical price of a bond, just like a stock, not only the risk-free interest rate, or yield, is used, but also the rate taking into account one or another level of risk inherent in the bond. In this sense, the models related to the share price, the model of linking profitability and risk in general, or factor risk in particular, are applicable to bond pricing. However, due to the existing differences between bonds and shares, accounting for risk in the bond price has its own peculiarities.
Table 1. Types of bonds| By the method of provision: |
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| By date: |
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| By the method of redemption of the par value (bond redemption): |
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| By income payment method: |
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The value of a bond as an asset is much easier to assess than, for example, a stock. The bond has a final maturity, the flow of payments (coupon payments) is in most cases fixed (as opposed to share dividends). There are significantly fewer risk factors and uncertainties than in the case of stocks.
Types of bond value:
· nominal
· "Clean"
· "Dirty"
When issued, bonds are placed, as a rule, at par or with a slight deviation from par - with discount or premium(only discount bonds for which no interest is paid are always placed at a price below par).
However, in the future, their price may deviate quite noticeably from the nominal. Take a classic coupon bond as an example. What are the factors underlying the dynamics of its price?
The main factor- this is the ratio of the market, i.e. current, interest rate and the coupon rate for the bond.
The 25-year bond was issued in 1990 during a period of relatively high interest rates in the world market. This means that in order to buy it, the issuer had to set a high coupon rate on it as well. Suppose the bond was floated at $ 1000 par with a coupon rate of 10%. By 2012, interest rates in the market fell. Bonds of issuers with a similar rating (i.e. with the same level of risk) are issued at a rate of 4% per annum. If our investor, who had an old bond, wants to sell it, he can do it not for $ 1000, but for a higher price - one that will provide an approximate yield of 4%. If the market discovers instruments that provide more high profitability than others, then everyone starts to buy this instrument, due to which prices equalize.
The dependence of the bond price on the coupon rate, bond maturity and the current market interest rate is described by a formula based on a compound interest discount formula.
Insert
In the previous example, we will find the price of this bond if there are still three years left until its maturity.
R = 100/1,04 + 100/1,08 + (100 + 1000)/1,125 = $1166,52.
In some cases, the net price formula needs to be clarified.
1. The coupon is paid several times a year. As already indicated, the coupon rate for the bond is announced as an annual percentage. In case the coupon is paid several times a year, the rate is divided by the number of payments. For example, a 10% coupon is paid twice a year. This means that every six months the issuer pays 5% of the bond's par value. In this case, in assessing the net worth of the bond, each payment must be discounted. But it should be borne in mind that the discount rate (market yield), which is in the denominator of the formula, is also indicated as an annual percentage, so it must also be divided by the number of coupon payments per year.
Thus, the formula is converted:
,
where R- bond price;
WITH- the amount of the coupon payment;
r - the required rate of return in the form of a decimal fraction;
N- bond par value;
n- the number of years to maturity;
m- the number of payments per year.
Differences between bonds and stocks
Shares are issued only by joint stock companies, bonds - by any commercial organization and the state.
The purpose of the issue of both shares and bonds is to raise free capital in small portions, but from many owners on the terms of payment of a certain type of income. However, if for a share the issuer provides for the payment of its par value (or other monetary amount) only in the event of liquidation of the joint-stock company, then for the bond it is mandatory to pay its par value upon its redemption (redemption).
Joint-stock companies have certain restrictions on the issue of their bonds, the main of which are that the par value of the issued bonds cannot exceed the size of the authorized capital of the company, which must be fully formed by the time the bonds are issued.
Types of bonds
1. By security:
1. classic (unsecured) - such bonds give the owner the right to receive income, and the return of the invested amount is set upon placement.
Unsecured bonds do not have any collateral and are guaranteed by the overall high credit rating of the issuer and its image as a company fully meeting its market obligations;
2. secured, giving the same rights to the owners as classical, as well as the right to receive a part of the property of the issuer, which he offers as security.
By issuers
· Government bonds(English Government bonds) or sovereign bonds (English Sovereign bonds) - a security issued to cover budget deficit on behalf of the government or local authorities, but necessarily guaranteed by the government.
Municipal bonds
By type of income
· Discount bond (eng. Zero Coupon Bond) - a bond, the income for which is a discount (zero coupon bond). Discount bonds are sold at below par. The closer the bond's maturity date, the higher the bond's market price. Examples of discount bonds - GKO, BOBR.
Fixed rate bond (eng. Fixed Rate Bond; Fixed Income) is a coupon bond, the yield on which is paid on coupons with a fixed interest rate. Information on coupons is indicated in the bond issue prospectus. This type of bonds includes OFZ, OVGVZ, most Eurobonds.
· Bond with floating interest rate (eng. Floating Rate Note (FRN); Floater) is a coupon bond with a variable coupon payment, the size of which is tied to certain macroeconomic benchmark indicators: to the yield on government securities, to interbank loan rates (LIBOR, EURIBOR, MOSPRIME), etc. The rate on coupon payments is regularly recalculated: usually monthly or every three months, etc.
By convertibility
· Convertible bonds - a debt instrument with a fixed interest rate, which gives the holder the right to exchange bonds and coupons for a certain number of ordinary shares or other debt instruments of a given issuer at a predetermined price (conversion price) and not earlier than a predetermined date. After conversion, the bond ceases to exist, and with it the issuer's debt. Convertible bonds are issued by both governments and companies.
· Non-convertible bonds.
By income payment method:
§ only interest is paid, the repurchase period is not specified (perpetual bonds);
§ bonds with a zero coupon - no interest payments are provided on them;
§ interest is paid together with the face value at the end of the term;
§ Interest is paid periodically throughout the entire term, and at the end of the term, the face value or redemption price is paid (this type of bond is most popular).
Valuation bonds.
Bond par value (face value) - the amount of money indicated on the bond, which the issuer borrows and promises to pay at the expiration a certain period(maturity).
Coupon interest rate - the ratio of the amount of interest paid to the par value of the bond. The higher the coupon interest rate, the higher the market value of the bond.
Basic rules to consider in the bond market:
§ the closer the maturity date at the time of purchase of the bond, the higher its market value;
§ the higher the income brought by the bond, the lower its market value;
Basic designations:
§ - current market interest rate
§ - coupon interest rate
§ - the par value of the bond
§ - the remaining term to maturity of the bond (years)
§ - the current market value of the bond
§ - coupon payment
§ r - income to maturity.
Formula of the current market value of a bond
The par value of the bond, the coupon interest rate, the remaining maturity of the bond of the year, the current market interest rate. Let's determine the current market value of the bond.
Amount of coupon payments:
Market price bonds:
The yield to maturity is calculated using the formula:
r = 
3.4. DERIVATIVE SECURITIES: FUTURES AND OPTIONS
Derivative security- this is a documentary or non-documentary form of expression of property rights (obligations) arising in connection with a change in the price of the exchange-traded (financial or commodity) asset underlying this security.
Derivative securities are a class of securities, the purpose of circulation of which is to extract profit from fluctuations in the prices of the corresponding exchange-traded asset.
Those. derivative securities – this is a contract for any price assets: commodity prices(usually, exchange commodities: corn, meat, oil, gold etc.); prices of underlying securities(usually, on bonds, on stock indices); credit market prices (interest rates); Prices currency market (exchange rates) etc.
Features of derivative securities:
Their price is based on the price of the underlying exchange asset;
Have a limited time period of existence;
Their purchase and sale allows you to make a profit with minimal investment in comparison with other securities, since the investor does not pay the entire value of the asset, but only the guarantee (margin) fee.
There are two types of derivatives: futures contracts, stock options. However, the emergence of these derivatives and the development of their exchange turnover was preceded by the practice of concluding forward contracts in the OTC market.
Forward contract is an agreement between two parties on the future delivery of the subject of the contract (securities, currencies, goods). This agreement is concluded outside the exchange.
Therefore, let's take a closer look at exchange contracts.
Futures contract is an agreement between two parties on the future delivery of the subject of the contract, concluded on the exchange.
Futures contract properties:
1. It is concluded on the exchange in accordance with the conditions adopted on it, therefore it is highly liquid.
2. It is standard, that is, an investor can easily buy or sell a futures contract (open a position) and subsequently liquidate his position by a reverse transaction.
3. Conclusion of futures deals is not aimed at real buying and selling an asset, but hedging positions or playing on price differences. Hedging - minimization (offset) of the price risk for a cash position by opening an opposite - term or option position for the same commodity or financial instrument with its subsequent offset (the task is to fix a certain price level). Since the standard terms of the contract are not always acceptable to the parties, only 2-5% of futures contracts for which positions remained open end with the actual delivery of the asset.
4. The execution of the futures contract is guaranteed by the clearing house of the exchange. This is ensured by the presence of a large insurance fund, the obligatory mechanism of the guarantee pledge (margin), as well as doubling when registering a futures contract concluded in the course of exchange trading in the clearinghouse:
The contract between the buyer of the primary asset and the clearinghouse as the seller;
The contract between the seller of the primary asset and the clearinghouse as the buyer.
The person who undertakes to buy the asset borrows long position, that is, buys a contract (the buyer of the contract). The person who undertakes to deliver the asset borrows short position, that is, sells a futures contract (the seller of the contract).
5. The basis of a futures contract is a limited range of primary assets, the main feature of which is the unpredictability of price changes. Futures contracts are concluded for such assets as agricultural goods (grain, etc.), natural resources (copper, gold, etc.), foreign currency, securities, market indices.
Standard parameters for trading futures contracts:
1. Trading party is the amount of the underlying asset included in one contract;
2. Place of delivery used in commodity futures. The sellers of contracts, who have not closed their positions, deliver the goods to the specified warehouse of the exchange;
3. Price quotation- the degree to which the price accuracy is determined (usually the price is determined with an accuracy of hundredths);
4. Price step- the minimum value of the price change per unit of the underlying asset is determined by the exchange independently and ensures the convergence of the buyer's and seller's prices during trading;
5. Standards are used in commodity futures trading and characterize the quality of the commodity underlying the futures contract. The standards have a class and a number (for example, for wheat, class: dark, northern No. 1);
6. Limit price changes in one day are set by the exchange independently in relation to the quoted price of the previous day. This indicator is introduced in order to limit speculation on a futures contract. If the futures price goes beyond the specified interval, then the exchange stops trading either until the end of the trading day, or for several days until the price enters the specified interval;
7. Planned months- months of execution of futures contracts (the date of the month is not indicated);
8. Last trading day, when contract positions can be liquidated (closed). Installed by the exchange itself. For example, a contract signed for May can be bought or sold no later than the seventh business day from the end of May;
9. Trading hours- on the exchange, futures for a specific asset are traded at specific hours. On the last trading day, trading ends, usually at noon;
10. Last day of delivery usually coincides with the last business day of the month in which the asset is to be delivered;
11. Positional limit is a limitation on the total number of contracts that one investor can keep open.
There are two main purposes of entering into futures contracts: hedging and speculation. Hedgers buy and sell futures to eliminate a risky position in the current market. In the normal course of business, they either sell or produce the underlying asset. Speculators buy and sell futures only for the purpose of getting a profit, closing their positions at a better price than the initial one.
Futures price is the price that is fixed when a futures contract is entered into. Represents the investor's expectation of the future current price.
The value of a futures contract can be defined as such a price at which the investor is equally profitable as buying the asset itself in the physical market and then storing it until it is used or earning income on it, or buying a futures contract for this asset.
The value of a futures contract is determined by such main factors as:
The price of an asset in the physical market;
The duration of the futures contract;
Interest rate;
The costs associated with owning an asset (storage, insurance).
To these factors, taking into account the specific specifics of the market and country, others can be added:
Differences in commission costs in the cash and futures markets;
Differences in taxation;
Differences in exchange rates and etc.
The mathematical calculation of the value of a futures contract depends on what factors are taken into account. For example, accounting for constant factors can be carried out according to the formula
, (6.1)
where C a is the cost of a futures contract for an exchange-traded asset A;
CA - the market price of asset A in the physical market;
P - bank interest on deposits;
D is the number of days before the expiration of the futures contract or its closure.
Rice. 9. Factors affecting the value of the contract
If the exchange asset itself brings certain income, for example, dividend on a stock or interest on a bond, then this income should be deducted from the bank interest rate, and the previous formula will take next view:
, (6.2)
where Pa - the average size dividend on a stock or interest on a bond.
For example, P a = 100 rubles, P = 20% per annum, P a = 10% (per year), D = 60 days. Substituting these values into formula (6.2), we calculate the value of a futures contract for the purchase of one share at the current market price of 100 rubles. and with an annual dividend of 10% with delivery in 60 days with an average market percentage 20% per annum:
The current day's market price for this futures contract will fluctuate under the influence of supply and demand around this calculated value.
Until the futures contract expires, there is a difference between its price and the price of its asset in the physical market, and the difference between the indicated prices is called basis of a futures contract:
, where B is the basis.
where C fk is the price of a futures contract for asset A;
C a - the price of asset A in the physical market.
Option- a contract between two investors, one of whom writes and sells an option, and the other buys it and gets the right to buy or sell an asset at an agreed price to the seller of the option within the period specified in the agreement.
Features of options and basic concepts.
1. An option is the right to buy or sell a title of property.
2... Option buyer- an investor who receives the right to buy (sell) an asset at a certain price.
3.Option seller (element)- an investor who wrote an option, received a premium for it and committed to sell (buy) an asset at the request of the option buyer.
4... Premium (option price)- the option price paid to the seller in exchange for the option certificate. It is set per unit of the underlying asset.
5. Operations with options are highly profitable, since by paying a small premium for an option, the investor, in a favorable case, makes a profit, which, as a percentage of the premium, can amount to hundreds of percent.
6. The risk of operations with options for the buyer is minimal and is measured by the amount of the premium paid (the cost of acquiring the contract).
7. An option provides its buyer with a multivariate choice of strategies: buy and sell options with different strike prices and delivery times in all possible combinations.
By terms of exercise, options are divided into two types:
- American option can be exercised on any day during the term of the option;
- European option is executed on the day the option expires.
Most option contracts are American in style.
If an investor buys an option, he is long. If he writes or sells, he is short.
There are two types of options:
1. Option to buy ("call") grants the owner the right to buy the underlying asset from the option seller at the price specified in the contract. The buyer pays the premium to the seller; the seller is obliged to sell the underlying asset at the first request of the option owner.
If we designate the price of an asset under an option contract as X; P is the price at the time the option is exercised; i is the premium paid for the option, then the following generalizations can be made:
If P> X, then the buyer's financial result is (P - X - i);
If P X, then the financial result is (- i).
Financial results the seller of the option will be:
When P> X - (X - P + i);
At Р X - (+ i).
2. Option to sell ("put")- gives the owner the right to sell the underlying asset at an agreed price to the seller of the option. The seller is obliged to buy the asset at the first request of the option owner.
Financial result of the buyer of the put option:
If P< Х - (X - P - i);
If P> X - (- i).
The seller's bottom line will be the opposite.
Since the option price may differ from the current market price (SPOT) at the time the option is issued, the following option categories are distinguished:
1. Winning Option- if the option is exercised immediately, the investor makes a profit. In this case, for the call option P> X, for the put option P<Х.
2. No Win Options - with immediate implementation, the financial result is zero P = X.
3. Losing options - immediate execution will result in losses. In this case, for the call option P<Х, для опциона "пут" Р>NS.
Stock options... Usually, the exchange establishes a list of companies whose shares are included in its listing and for which the conclusion of option contracts is allowed. Depending on the market price of each type of shares, options may differ in the number of shares for which the option is concluded. As a rule, this amount is standard and is 100 or 1000 shares.
Essential characteristics of a stock option:
- option price- the premium per share depends on the type of option, delivery month and strike price;
- corresponds to the minimum change in the share price;
- - product of the price step by the number of shares underlying the contract;
- usually three months;
- option exercise- physical delivery of shares at the option exercise price.
Index options... Index options are usually traded on the same stock indices as futures contracts. This provides additional opportunities for hedging and speculative strategies based on combinations of futures contracts and index options.
Essential characteristics of an index option:
- option price- premium in index points, i.e. expected change in the index;
- minimum change in the option price (step) corresponds to the minimum change in the index;
- minimum change in contract value- product of the price step by the monetary factor;
- the period for which the option is concluded,- usually three months;
- option exercise- no physical delivery. A contract is settled according to the difference between its strike price and the market value of the index on the day the option is exercised.
Interest rate options... This is a wide class of options based on changes in the price of various kinds of debt obligations: short-term, medium-term and long-term bonds of the federal government, local governments, as well as mortgage bonds.
Standard characteristics of an interest rate option:
- option price- premium in index points, i.e. the expected change in the price of the bond, expressed as a percentage of its par value;
- minimum change in the option price (step) corresponds to the minimum change in the price of a debt instrument;
- minimum change in contract value- product of the price step by the monetary factor (bond par value);
- the period for which the option is concluded - usually three months;
- option exercise- physical delivery of debt obligations at the option exercise price.
Foreign exchange options- a class of options based on the change in the exchange rates of freely convertible currencies in relation to the national currency. Standard characteristics of a currency option:
- option price- premium per unit of currency;
- minimum change in the option price (step) corresponds to the minimum change in the exchange rate;
- minimum change in contract value- product of the price step by the amount of currency underlying the contract;
- the period for which the option is concluded,- usually three months;
- option exercise- physical delivery of the relevant currency or payment of the difference between the market rate and the strike price of the option in favor of the winning party of the option contract.
Options on futures contracts- a class of options concluded on existing types of futures. An option on a futures gives the right to buy or sell the corresponding futures contract at the strike price of the option. The exercise of such an option means that the option is exchanged for a futures contract.
In this case, the buyer of the call option has the right to become a buyer under a futures contract with the expiration date in the same month as the expiration date of the option, and the seller of the option is obliged to become the seller under this futures contract.
In contrast, the buyer of the put option has the right to become the seller of the futures contract with the expiration date of the latter in the same month as the expiration date of the option, and the seller of the option is obliged to become the buyer of the futures contract.
Standard features of a futures option:
- option contract size- one futures contract for stock values or currency;
- option price- premium per unit of the underlying asset;
- minimum change in the option price (step) corresponds to the minimum change in the value of the underlying asset;
- minimum change in contract value- product of the price step by the asset value;
- the period for which the option is concluded,- usually three months;
- calculations- payment of margin payments by the seller and the buyer of the option on the market of this futures contract;
- option exercise:
Conclusion of a futures contract;
Payment of the difference between the market rate (price) of an asset and the strike price of an option.