Weapons of a cautious investor: we consider the fair value of investment bonds
Hi, Habr! Today we want to raise a rather non-standard topic for a blog - investment bonds. Why did we decide to write about it? The topic of structural financial products, which include investment bonds, has recently become increasingly popular, and there is very little clear information that this and how this tool works. Interested? Welcome under cat.
What is an investment bond (IO)? In a general sense, this is a “hybrid” of a bond and an option.
With a classic bond, it is related by the fact that the issuer undertakes to pay the nominal value (redeem the bond) after the deadline. However, depending on the conditions defined in the prospectus, the paper can be redeemed and at a cost below par.
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As in conventional bonds, coupon payments are provided for investment bonds. Their parameters are described in the prospectus. However, the rate on them, as a rule, is small and significantly lower than the key rate of the Central Bank. Instead, the investment income of the instrument is tied to a certain underlying asset - this is the relationship between IO and options.
The underlying asset for an investment bond may be, for example, shares of some companies (for example, Sberbank, Gazprom, Apple or Agricultural Bank of China) or stock indices (S & P500, Nasdaq Composite, MICEX index or FTSE100). Depending on the value of the underlying asset at the maturity date, and determined by investment income, which will receive or not receive the owner of the paper.
For players who are not willing to risk their capital, but are interested in betting on some investment idea, this is a very convenient scheme. Imagine: an investor is confident that Amazon / Netflix / Tesla shares ... will grow by at least 30% over the next 2 years. But he is not ready to buy paper directly, because he is afraid of losing his savings, or he does not have time for weekly tracking of quotations and constant analysis of the news flow.
Investment bonds are a good way to test your investment idea. If the rate of the underlying asset does not increase or even fall, the investor will still return his money when redeeming the bonds and will not lose anything, except the time value of money (of course, the risk of defaulting the issuer of the paper should also be taken into account). If the price of the underlying asset to which investment income is tied increases, the investor will receive a profit.
This is critical for unqualified investors who are just starting to invest in risky assets, or for more experienced investors if they want to change the risk profile of their portfolio. Of course, it should be borne in mind that a significant reduction in risk means a decrease in expected income - this basic rule for evaluating financial instruments also applies here.
Thus, if we compare the IO with ordinary bonds and deposits, it can be noted that due to the more flexible payments on structural bonds, the IO allows us to form a more favorable risk-return ratio . Therefore, the Oncological Institute is likely to continue to gain popularity.
As a rule, most investors cannot create a portfolio of tools similar to the EUT. The nomenclature and liquidity on option boards on stock exchanges is limited. Moreover, options built into an IO can have an exotic structure. But by adding such a tool to your portfolio, an investor can create a paper that plays out his investment idea with the appropriate ratio of risk and return. As an example, IO with a coupon with a memory (memory coupon) or an IO with built-in barrier knock-in options.
The main buyers of investment bonds are private and professional investors, the main issuers are financial companies. Papers are placed, as a rule, on the over-the-counter market in the format of the so-called Principal Protected Notes. But there are also bonds traded on exchanges. In Russia, due to the peculiarities of regulation, this option has become more common.
Anyone can see the quotes of the Oncological Institute on the Moscow State Exchange .
This is very good news. Due to the fact that IO mainly bargains on the stock exchange, in the secondary market almost anyone can buy or sell them if it suits the current price.
When placing investment bonds, the issuer charges a commission. It should be borne in mind: the smaller the volume of a single transaction with such a “customized” IO, the higher the commission will be. In essence, the commission is the payment for the services of the team of traders and managers who formed this structured product. For investors with a small capital, a profitable solution may be participation in public offerings of the Oncological Institute. Banks offer such papers in large volumes and spend a lot of resources on optimizing the tool. If the client as a whole agrees with the investment idea of the product, participation in the pool of buyers will reduce his commission.
Since the income that an investment bond will bring (or not bring) to its owner depends directly on the value of the underlying asset, such a binding can be considered as an option embedded in the paper. In order to correctly determine the value of the paper, it is necessary to “divide” it into two components - interest and derivative.
The interest component is estimated by discounting future payments along a certain yield curve. As a rule, this is a risk-free return curve to which the counterparty credit spread is added.
The derivative part of the EUT often consists of a set of various embedded options. Their price and risk metrics will be calculated using various valuation methods. For example, if a simple call or put option is used, then most often its price will be determined through the Black-Scholes model.
It should be noted that, in most cases, the use of the Black-Scholes approach is a strong simplification. For example, in the case of IO, since they most often have a long maturity, the Black-Scholes model is no longer adequate for their evaluation. Also, sometimes the calculation requires taking into account in addition to the stochastic evolution of the underlying asset and the evolution of interest rates, exchange rates and other market factors. In this case, the parameters of evolution can, in turn, be random processes at all. Therefore, other methods are most often used to determine prices and risk metrics. As a rule, numerical: trees (for example, binomial), Monte-Carlo approaches.
When calculating the price, sometimes you also need to consider the credit properties of the issuer of the Oncological Institute. The so-called CVA amendments are responsible for this. Numerical methods are also used to calculate them, and due to some peculiarities of these corrections, these methods must be very efficient from a computational point of view.
Now there is a fairly wide range of tools that allow if you do not solve such problems completely, then at least have a certain framework to get started. These are vendor products with proprietary code (for example, Bloomberg), which are often offered as services, and open-source libraries (such as QuantLib). As a rule, banks actively operating in this market develop their own libraries for the valuation and risk management of exotic options that integrate with all front and back office systems.
Let's look at the IO, which is tied to the behavior of the S & P500 index and pays an additional coupon yield, proportional to the index yield in the event of its positive dynamics. Simply put, a potential investor buys this tool, hoping to earn on the growth of the S & P500 index.
For example, at the time of issuing an IO, the index value is 2500 points. Let the IO payment be built so that at the time of redemption additional income will be paid only if the index value is above 2500. That is, if the index is below this bar, then at the time of redemption only the nominal value of the bond will be returned to the owner. If at the time of redemption S & P500 will be equal to 3000, then the additional coupon payment will be equal to from face value of the bond.
Suppose we want to purchase such an IO with a nominal value of 1000 rubles. Suppose a year has passed since the issue, a year remains until the end of the redemption, and now the S & P500 is equal to 2800. What is the fair value of the paper?
The payment on the EA in a year is equal to
Note that the last term is a payment on the call option. Suppose the time value of money is determined by the risk-free rate r, as a proxy for it we take the key rate of the Central Bank = 7.75%. Then the fair value of the bond without taking into account the issuer's credit risk is now equal to:
, here EV is a mathematical expectation by some probability measure.
If the market value of the paper is below this level, obviously, its purchase is generally reasonable. Here the option is calculated using the Black-Scholes formula.
In this post we presented investment bonds and outlined the most necessary things about them. Further, it is worth considering the methods for estimating the value of options embedded in the EUT. This is a big hot topic. In the open access contains only basic information or offers from vendors. If the topic is interesting, we will definitely continue its research, but for now we are ready to answer your questions.
Bond + Option
What is an investment bond (IO)? In a general sense, this is a “hybrid” of a bond and an option.
With a classic bond, it is related by the fact that the issuer undertakes to pay the nominal value (redeem the bond) after the deadline. However, depending on the conditions defined in the prospectus, the paper can be redeemed and at a cost below par.
')
As in conventional bonds, coupon payments are provided for investment bonds. Their parameters are described in the prospectus. However, the rate on them, as a rule, is small and significantly lower than the key rate of the Central Bank. Instead, the investment income of the instrument is tied to a certain underlying asset - this is the relationship between IO and options.
The underlying asset for an investment bond may be, for example, shares of some companies (for example, Sberbank, Gazprom, Apple or Agricultural Bank of China) or stock indices (S & P500, Nasdaq Composite, MICEX index or FTSE100). Depending on the value of the underlying asset at the maturity date, and determined by investment income, which will receive or not receive the owner of the paper.
For players who are not willing to risk their capital, but are interested in betting on some investment idea, this is a very convenient scheme. Imagine: an investor is confident that Amazon / Netflix / Tesla shares ... will grow by at least 30% over the next 2 years. But he is not ready to buy paper directly, because he is afraid of losing his savings, or he does not have time for weekly tracking of quotations and constant analysis of the news flow.
Investment bonds are a good way to test your investment idea. If the rate of the underlying asset does not increase or even fall, the investor will still return his money when redeeming the bonds and will not lose anything, except the time value of money (of course, the risk of defaulting the issuer of the paper should also be taken into account). If the price of the underlying asset to which investment income is tied increases, the investor will receive a profit.
This is critical for unqualified investors who are just starting to invest in risky assets, or for more experienced investors if they want to change the risk profile of their portfolio. Of course, it should be borne in mind that a significant reduction in risk means a decrease in expected income - this basic rule for evaluating financial instruments also applies here.
Thus, if we compare the IO with ordinary bonds and deposits, it can be noted that due to the more flexible payments on structural bonds, the IO allows us to form a more favorable risk-return ratio . Therefore, the Oncological Institute is likely to continue to gain popularity.
As a rule, most investors cannot create a portfolio of tools similar to the EUT. The nomenclature and liquidity on option boards on stock exchanges is limited. Moreover, options built into an IO can have an exotic structure. But by adding such a tool to your portfolio, an investor can create a paper that plays out his investment idea with the appropriate ratio of risk and return. As an example, IO with a coupon with a memory (memory coupon) or an IO with built-in barrier knock-in options.
The main buyers of investment bonds are private and professional investors, the main issuers are financial companies. Papers are placed, as a rule, on the over-the-counter market in the format of the so-called Principal Protected Notes. But there are also bonds traded on exchanges. In Russia, due to the peculiarities of regulation, this option has become more common.
Anyone can see the quotes of the Oncological Institute on the Moscow State Exchange .
This is very good news. Due to the fact that IO mainly bargains on the stock exchange, in the secondary market almost anyone can buy or sell them if it suits the current price.
When placing investment bonds, the issuer charges a commission. It should be borne in mind: the smaller the volume of a single transaction with such a “customized” IO, the higher the commission will be. In essence, the commission is the payment for the services of the team of traders and managers who formed this structured product. For investors with a small capital, a profitable solution may be participation in public offerings of the Oncological Institute. Banks offer such papers in large volumes and spend a lot of resources on optimizing the tool. If the client as a whole agrees with the investment idea of the product, participation in the pool of buyers will reduce his commission.
Theory: How to Estimate the Fair Value of IO
Since the income that an investment bond will bring (or not bring) to its owner depends directly on the value of the underlying asset, such a binding can be considered as an option embedded in the paper. In order to correctly determine the value of the paper, it is necessary to “divide” it into two components - interest and derivative.
The interest component is estimated by discounting future payments along a certain yield curve. As a rule, this is a risk-free return curve to which the counterparty credit spread is added.
The derivative part of the EUT often consists of a set of various embedded options. Their price and risk metrics will be calculated using various valuation methods. For example, if a simple call or put option is used, then most often its price will be determined through the Black-Scholes model.
It should be noted that, in most cases, the use of the Black-Scholes approach is a strong simplification. For example, in the case of IO, since they most often have a long maturity, the Black-Scholes model is no longer adequate for their evaluation. Also, sometimes the calculation requires taking into account in addition to the stochastic evolution of the underlying asset and the evolution of interest rates, exchange rates and other market factors. In this case, the parameters of evolution can, in turn, be random processes at all. Therefore, other methods are most often used to determine prices and risk metrics. As a rule, numerical: trees (for example, binomial), Monte-Carlo approaches.
When calculating the price, sometimes you also need to consider the credit properties of the issuer of the Oncological Institute. The so-called CVA amendments are responsible for this. Numerical methods are also used to calculate them, and due to some peculiarities of these corrections, these methods must be very efficient from a computational point of view.
Now there is a fairly wide range of tools that allow if you do not solve such problems completely, then at least have a certain framework to get started. These are vendor products with proprietary code (for example, Bloomberg), which are often offered as services, and open-source libraries (such as QuantLib). As a rule, banks actively operating in this market develop their own libraries for the valuation and risk management of exotic options that integrate with all front and back office systems.
Practice: how to evaluate the fair price of an IO
Let's look at the IO, which is tied to the behavior of the S & P500 index and pays an additional coupon yield, proportional to the index yield in the event of its positive dynamics. Simply put, a potential investor buys this tool, hoping to earn on the growth of the S & P500 index.
For example, at the time of issuing an IO, the index value is 2500 points. Let the IO payment be built so that at the time of redemption additional income will be paid only if the index value is above 2500. That is, if the index is below this bar, then at the time of redemption only the nominal value of the bond will be returned to the owner. If at the time of redemption S & P500 will be equal to 3000, then the additional coupon payment will be equal to from face value of the bond.
Suppose we want to purchase such an IO with a nominal value of 1000 rubles. Suppose a year has passed since the issue, a year remains until the end of the redemption, and now the S & P500 is equal to 2800. What is the fair value of the paper?
The payment on the EA in a year is equal to
Note that the last term is a payment on the call option. Suppose the time value of money is determined by the risk-free rate r, as a proxy for it we take the key rate of the Central Bank = 7.75%. Then the fair value of the bond without taking into account the issuer's credit risk is now equal to:
, here EV is a mathematical expectation by some probability measure.
If the market value of the paper is below this level, obviously, its purchase is generally reasonable. Here the option is calculated using the Black-Scholes formula.
Conclusion
In this post we presented investment bonds and outlined the most necessary things about them. Further, it is worth considering the methods for estimating the value of options embedded in the EUT. This is a big hot topic. In the open access contains only basic information or offers from vendors. If the topic is interesting, we will definitely continue its research, but for now we are ready to answer your questions.
Source: https://habr.com/ru/post/454788/
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