Thursday, December 31, 2009

(115)---FACTORS DETERMINING OPTION VALUE

Factors Determining Option Value

The seller of an option gives away the good outcomes of the asset held by him to the option buyer for a price or premium.

How is this price or premium determined? The value of a call option at maturity is either zero or the difference between the price of the share (that is, the underlying asset) and exercise price. Thus,

Value of call option = Maximum share price – Exercise price

The option holder will exercise his option only when it is beneficial to do so. The call option will be beneficial to its buyer when the exercise price is less than the price of the share (the underlying asset). When the call option is out of the money (the exercise price is more than the price of the underlying asset), the minimum value of the call option at expiration will be zero.

How is the value of an option with time to expiration determined?

The value of an option depends on the following factors,
  1. Exercise price and the share (underlying asset) price
  2. Volatility of returns on the share
  3. Time to expiration
  4. Interest rates


Exercise price and value of underlying asset

Two important determinants of options are the value of the underlying asset and the exercise price. If the underlying asset were share, the value of a call option would increase as the share price increases. At the expiration date, the holder will know the share price, and he will exercise his option if the exercise price is lower than the share price. The excess of the share price over the exercise price is the value of the option at the expiration of the option. If the share price is more than the exercise price, a call option is said to be in the money. The deeper in the money is an option, the more is its value.


Volatility of underlying asset

How is the value of a call option affected by the volatility of the underlying asset? Let us consider an example.

Suppose you hold a two 2 months option on the share of Company Y. The exercise price is 100$ and the current market price is 100$. The option will be worthless if the share price remains 100$ at maturity. But prior to expiration, the option will be valuable if there are chances that the share price may rise above 100$.


Time to option expiration

The present value of the exercise price also depends on the time to expiration of the option. The present value of the exercise price will be less if time to expiration is longer and consequently, the value of the option will be higher. Further, the possibility of share price increasing with volatility increases if the time to expiration is longer. Longer is the time to expiration, higher is the possibility of the option to be more in the money.


Interest rates

The holder of a call option pays exercise price not when he buys the option, rather, later on, when he exercises his option. Thus, the present value of the exercise price will depend on the interest rate. The value of a call option will increase with the rising interest rate since the present value of the exercise price will fall. The effect is reversed in the case of a put option. The buyer of a put option receives the exercise price and therefore, as the interest rate increases, the value of the put option will decline.

Monday, December 28, 2009

(114)---STRIPS AND STRAPS

Strips and Straps

You can design strategies that are variations of a straddle. Strips and straps are two such variations.

A strip is a combination of two puts and one call with the same exercise price and expiration date.

A strap, one of the other hands, entails combining two calls and one put.

We assume that the exercise price for puts and calls is 100$ and that share price at expiration is 90$, 100$ or 110$. The investor would have positive pay off irrespective of the price movement, expect when the price equals the exercise price. The potential pay off would be higher under a strap strategy for share price above the exercise price.

Strangle: Combining call and put at different exercise prices

A strangle is a portfolio of a put and a call with the same expiration date but with different exercise prices.

The investor with combine an out of the money call with an out of the money put. That is, he will buy a call with an exercise price higher than the underlying share’s current price and a put with an exercise price lower than the underlying share’s current price. The effect of this strategy is similar to the effect of a straddle expect that the pay off range will be larger.

Spread: Combining put and calls at different exercise prices

The put and call options on the same share may have different exercise prices, and an investor may combine them. A spread is a combination of a put and a call with different exercise prices.

Saturday, December 26, 2009

(113)---COMBINING CALL AND PUT OPTIONS AT THE SAME EXERCISE PRICE

Combining Call and Put Options at the Same Exercise Price

Suppose Company Y is considering the acquisition of Company X. It has offered to buy 20 percent of Company X shares. The price of Company X share has started increasing. The price could decline substantially if Company Y’s attempt fails.

How could you take advantages of rising prices and at the same time avoid the risk if the price falls? You can do so by simultaneously purchasing both put and call options at the same exercise price.

A company Y is a combined position created by the simultaneous purchase or sale of a put and a call with the same expiration date and the same exercise price.

Suppose the exercise price is 105$ for both put and call options. What will be your pay off if the price of Company X’s share increases to 120$ in three months? You will forgo put option, but you will exercise call option. So your pay off will be the excess of the share price over the call exercise price 120$-105$=15$.

On the contrary, suppose that the acquisition attempt fails and Company X share price falls to 95$ in three months. In this situation, you will exercise put options and let the call option lapse. Your pay off will be the excess of exercise price over the share price 105$-95$=10$. Thus, when you invest in a Company Y, you will benefit whether the price of the share falls or rises.

What will be the position of the seller of a company Y? He will lose whether the price of the share increases or decreases. But the seller of a Company Y will collect put and call premium. Thus, his lose will be reduced or his net pay off may be even positive.

Thursday, December 24, 2009

(112)---BUYING A SHARE AND SELLING A CALL

Buying a Share and Selling a Call

A naked option is a position where the option writer does not hold a share in her portfolio that has a counterbalancing effect. The investor can protect herself by talking a covered position.

A covered call position is an investment in a share plus the sale of a call on that share. The position is covered because the investor holds a share against a possible obligation to deliver the share. The total value or pay off of a covered call at expiration is the share price minus the value of the call.


The value of call is deducted because the investor has taken a short position; that is he is under an obligation to deliver the share to the buyer of the call option if he chooses to exercise his option. The buyer of the call will do so when the exercise price is lower than the share price.

An Example,


Assume that a call option is at the money; that is both the current price of the share and the exercise price is 100$. Further, suppose the possible share price at expiration is either 110$ or 90$.

When the share price is equal to or less than the exercise price, the investor’s pay off will equal to the share price.

The investor’s maximum pay off to a covered call cannot exceed the exercise price in the rising market. He sacrifices the opportunity of earning capital gains in favorable of enhancing the current income by premium. Investors who are in any case planning to sell shares at a price equal to the exercising price will follow the strategy.

Wednesday, December 23, 2009

(111)---COMBINATIONS OF PUT, CALL AND SHARE

Combinations of Put, Call and Share Options

Theoretically, an investor can from portfolio of options with any assets. In practice, stock options are most popular. A share, a put and a call can be combined together to create several pay off opportunities. Some of these combinations have significant implications.

Combination of share and a put option

A long position involves buying and holding shares or any other assets to benefit from capital gains and dividend.

An investor may create a long position in the shares of a firm. A long position investment strategy is risky.

The investor will incur loss if the share price declines. An investor will gain if the share price rises in the future. However, he will incur loss if the price in future turns out to be lower than the current price. An investor can however, guard himself against the risk of loss in the share value by purchasing a put option that has the exercise price equal to the current market price of the share.

Put option at the money is called a protective put. The combination of a long position in the share and a protective put helps to avoid the investor’s risk when the share price falls.

If the price of the share increases, the investor gains and the value of his portfolio at expiration will be equal to the share price.

The value of put to him will be zero since he will not exercise his options. On the other hand, if then share price falls, the value of the investor’s portfolio will be equal to the share price plus the value of the put option. Since the put was at the money when the investor sold it, the value of his portfolio will be at least equal to the share price at that time.

Monday, December 21, 2009

(110)---PUT OPTION

Put Option

A put option is a contract that gives the holder a right to sell a specific share or any other asset at an agreed exercise price on or before a given maturity period.

Suppose you expect price of company Y share to fall in the near future. Therefore, you buy a 3 month put option at an exercise price of 50$. The current market price of company Y share is 48$. If the price actually falls to 35$ after three months, you will exercise your option. You will buy the share for 35$ from the market and deliver it to the put option seller to receive 50$. Your gain is 15$, ignoring the put option premium, transaction cost and taxes.

You will forgo your put option if the share price rises above the exercise price; the put option is worthless for you and its value is zero. A put buyer gains when the share price falls below the exercise price. Ignoring the cost of buying the put option called put premium, his loss will be zero when the share prices rises above the exercise price since he will not exercise his option.

Put option pay off

An investor hopes that the price of company Y share will fall after three months. Therefore he purchases a put option on company Y share with a maturity of three months of premium of 5$. Then exercise price is 30$. The current market price of Company Y share is 28$. How much is profit or loss of the put buyer and the put seller if the price of the share at the time of the maturity of the option turns out to be 18$, or 25$, or 28$, or 30$, or 40$?

The put option buyer s maximum loss is confined to 5$ that is the put premium. His profit equal to exercise price less the sum of share price and premium. Since the share price cannot fall below zero, he has a limited profit potential. The put buyer will always exercise his option if the exercise is more than the share price. His break even share price is 25$ that is the exercise price premium.

For the seller of a put option, the profit will be limited to 5$ the amount of premium. His loss potential depends on the price of the share. But it cannot exceed 25$ that is the difference between the exercise price, 30$ and the premium 5$.

Saturday, December 19, 2009

(109)---CALL OPTION

Call Option

A call option on a share or any asset is a right to buy the share at an agreed exercise price. Suppose that the current share price of company X share is 130$. You expect that price in a three month period will go up to 150$. But you do fear that the price may also fall below 130$. To reduce the chance of your risk and at the same time to have an opportunity of marking profit, instead of buying the share, you can buy a three month call option on company X share at an agreed exercise price of, say, 125$.

Ignoring the option premium, taxes, transaction costs and the time value of money, will you exercise of your option if the price of the share is 130$ in three months?

You will exercise your option since you get a share worth 130$ by paying an exercise price of 125$. You will gain 5$ that is, the pay off or the value of your call option at expiration is 5$. Your call option is in the money at maturity.

What will you do if the price of the share is 120$ when the call option on company X expires?
Obviously, you will not exercise the option. You gain nothing. Your call option is worthless, and it is out of the money at expiration. You may notice that the value of your call option can never be less than zero.


Call Premium

A call buyer exercises his right only when the outcomes are favorable to him. The seller of call option, being the owner of the asset, gives away the good outcomes in favor of the option buyer. The buyer of a call option must, therefore, pay up front a price, called call premium, to the call seller to by the option.

The call premium is a cost to the option buyer and a gain to the call seller. What is the net pay off of the buyer and the seller of a call option when the call premium (that the buyer has to pay to the seller) in involved?

Friday, December 18, 2009

(108)---OPTIONS

Options

In a broad sense, an option is a claim without any liability. It is a claim contingent upon the occurrence of certain conditions. Thus, an option is a contingent claim. More specifically, an option is a contract that gives the holder a right, without any obligation, to buy or sell an asset at an agreed price on or before a specific period of time.

The option to buy an asset is known as a call option, and the option to sell an asset is called an exercise price or a strike price. The asset on which the put or call option is created is referred to as the underlying asset. Depending on when an option can be exercised, it is classified on two categories,
  • European option. When an option is allowed to be exercised only the maturity dates, it is called a European option.
  • American option. When the option can be exercised any time before its maturity, it is called an American option.

When will an option holder exercise his right? He will exercise his option when doing so provides him a benefit over buying or selling the underlying asset from the market at the prevailing price.
There are three possibilities,

  1. In the money. A put or a call option is said to in the money when it is advantageous for the investor to exercise it. In the case of in the money call options, the exercise price is less than the current value of the underlying asset, while in the case of the in the money put options, the exercise price is higher than the current value of the underlying asset.
  2. Out of the money. A put or a call option is out the money if it is not advantageous for the investor to exercise it. In the case of the out of the money call option, the exercise price is higher than the current value of then underlying asset, while in the case of the out of money put options, the exercise is lower than the current value of the underlying asset.
  3. At the money. When the holder of a put or a call option does not lose or gain whether or not he exercise his option, the option is said to be at the money. In the case of the out of the money options the exercise price is equal to the current value of the underlying asset.


Options do not come free. The involve cost. The option premium is the price that the holder of an option has to pay for obtaining a call or a put option. The price will have to be paid, generally in advance, whether or not the holder exercises his option.

Wednesday, December 16, 2009

(107)---OPTIONS AND THEIR VALUATION

Options and Their Valuation

Options mean things to different people. It may refer to choice or alternative or privilege or opportunity or preference right.

To have options is normally regarded good. One is considered unfortunate without any options. Options are valuable since they provide protection against unwanted, uncertain happenings. They provide alternatives to bail out from a difficult situation. Options can be exercised on happening of certain events.

Options may be explicit or implicit. When you buy insurance on your house, it is an explicit option that will protect you in the event there is a fire or a theft in your house. If you own share of a company, your liability is limited. Limited liability is an implicit option to default on the payment of debt.

Options have assumed considerable significance in finance. They can be written on any asset, including shares, binds, portfolios, stock indices, currencies excreta. They are quite useful in risk management. How are options defined in finance? What gives value to options? How are they valued?

Options

In a broad sense, an option is a claim without any liability. It is a claim contingent upon the occurrence of certain conditions.

Depending on when an option can be exercised, it is classified in one of the following two categories.
  • European option
    When an option is allowed to be exercised only on the maturity date, it is called a European option.
  • American option
    When the option can be exercised any time before its maturity, it is called American option.

Monday, December 14, 2009

(106)---CAPITAL ASSET PRICING MODEL AND THE OPPORTUNITY COST OF EQUITY

Capital Asset Pricing Model and the Opportunity Cost of Equity

Shareholders supply capital to a form. In return, they expect to receive dividends. They can also realize cash by selling their shares.

The firm has discretion to retain entire or a part of profits. If dividends were distributed to shareholders, they would have an opportunity to invest cash so receive in securities in the capital markets and earn a return.

When a firm retains profits, there is loss of opportunity for which shareholders need to be compensated. The expected rate of return from a security of equivalent risk in the capital market is the cost of the lost opportunity. Shareholders require the firm to at least earn this rate on their capital invested in projects.

From the firms point of view the expected rate of return from a security of equivalent risk is the cost of equity.

We need the following information to estimate a firms cost of equity,
  • The risk free rate
  • The market premium
  • The beta of the firms share

The use of the industry beta is preferable for those companies whose operations match up with the industry operations.

The industry beta is less affected by random variations. Those companies that have operations quite different from a large number of companies in the industry may stick to the use of their own betas rather than the industry beta.

Let us emphasize that there is no theory for the selection of beta. Beta estimation and selection is an art as well, which one learns with experience.

Sunday, December 13, 2009

(105)---DETERMINANTS OF BETA (2).

Determinants of Beta

As we discussed above beta depend on three fundamental factors: the nature of business, the operating leverage and the financial leverage. About the nature of business we discussed earlier, fro this post we discussing about other two factors.

Operating Leverage

Operating leverage refers to the use of fixed costs. The degree of operating leverage is defined as the change in an economy’s earning before interest and tax due to change in sales. Since variable costs change in direct proportion of sales and fixed costs return constant, the variability in earning before interest and tax when sales change is caused by fixed costs.

Higher the fixed cost, higher the variability in earning before interest and tax for a given change in sales. Other things remaining the same, companies with higher operating leverage are more risky.

Operating leverage intensifies the effect of cyclically on a company’s earnings. As a consequence, companies with higher degree of operating leverage have high betas.

Financial Leverage

Financial leverage refers to debt in a firm’s capital structure. Firms with debt in the capital structure are called leverage firms.

The interest payments on debt are fixed irrespective of the firm’s earnings. Hence, interest changes are fixed costs of debt financing. The fixed costs of operations result in operating leverage and caused earnings before interest and tax to vary with changes in sales.

Similarly, the fixed financial costs result in financial leverage and cause profit after tax to vary with changes in earning before interest and tax. Hence, the degree of financial leverage is defined as the change in a company’s profit after tax due to change in its earnings before interest and tax. Since financial leverage increases the firm’s financial risk, it will increase the equity beta of then firm.

Friday, December 11, 2009

(104)---DETERMINANTS OF BETA

Determinants of Beta

We have explained that beta is the ratio of covariance between returns on market and a security to variance of the market returns.

But what drives the variance and covariance? The variance and covariance and therefore, beta depend on three fundamental factors: the nature of business, the operating leverage and the financial leverage.
Those factors are discussed below.

Nature of Business

All economics go through business cycles. Firms behave differently with business cycles. The earnings of some companies fluctuate more with the business cycles. Their earnings grow during the growth phase of the business cycle and decline during the contraction phase.

For example, the earnings of consumer product firms or the cargo firms are tied with the business cycle and they go up or down with business cycle. On the other hand, the earnings of utility companies remind unaffected by the business cycle. If we regression a company’s earnings with the aggregate earnings of all companies in the economy, we would obtain a sensitivity index, which we can call the companies accounting beta. The real or the market beta is based on share market returns rather than earnings. The accounting betas are significantly correlated with the market betas.

This implies that if a firms earnings are more sensitive to business conditions, it is likely to have higher beta.

We must distinguish between the earnings variability and the earnings cyclically. A company’s earnings may be highly variable, but it may not have high beta. The earnings variability is an example of a specific risk that can be diversified. Cyclically of a companies earnings on the other hand, is the variability of its earnings Vi's-à-Vi's the aggregate earnings of the economy.

Wednesday, December 9, 2009

(103)---BETA ESTIMATING

Beta Estimation

Net present value of an investment is the discounted value of its future cash flows. The capital asset pricing model risk return framework provides us with a method of determining the discount rate of an investment.

The risk of a portfolio of securities is measured by its variance or standard deviation. The variance of a portfolio is the sum of;
  • The variances of individual securities times the square of their respective weight and,
  • The covariance that is the correlation coefficient between securities times their standard deviations of securities times twice the product of their respective weights.

In a well diversified portfolio the weights of individual securities will be very small and therefore, the variance of individual securities will be quite insignificant. But the covariance between the securities will be significant, and its magnitude will depend on the correlation coefficients between securities.

The covariance will be negative if all securities in the portfolio are negatively correlated. In practice, securities may have some correlation because they all have a tendency to more with the market.

This logic introduces the concepts of diversifiable risk and non diversifiable risk. The unique or the unsystematic risk of a security can be diversified when it is combined with other securities to form a well diversified portfolio.

On the other hand, the market or the systematic risk of the security cannot be diversified because like other securities, it also moves with the market.

There are two methods to calculate systematic risk of a security,

  1. Direct method.
  2. The market model.

Monday, December 7, 2009

(102)---STEPS IN CALCULATING EXPECTED RETURN UNDER ARBITRAGE PRICING THEORY

Steps in Calculating Expected Return under Arbitrage Pricing Theory

The following three steps are involved in estimating the expected return on an asset under Arbitrage pricing theory,
  1. Searching for the factors that affect the assets return
  2. Estimating of risk premium for each factor
  3. Estimating of factor beta

Factors

What factors are important in explaining the expected return? How are they identified? Arbitrage pricing theory does not indicate the factors that explain assets returns. The factors are empirically derived from the available data. Different assets will be affected differently by the factors.
The following factors were found important in a research study in the USA,

  • Industrial production
  • Changes in default premium
  • Changes in the structure of interest rates
  • Inflation rate
  • Changes in the real rate of return

Is this an exhaustive list of macro economic factors? All do not agree. In another study, it has been found that price to book value rations and sizes are correlated with the actual returns. These measures have been found as good proxy of the risk.

Risk premium

What is the risk premium for each factor? Conceptually it is the compensation, over and above the risk free rate of return that investors require for the risk contributed by the factor. One could use past data on the forecast ed and actual values to determine the premium.

Factors beta

The beta of the factor is the sensitivity of the assets return to the changes in the factor. We can use regression approach to calculate the factor beta. For example a firm’s returns could be regressed to inflation relate to determine the inflation beta.

Sunday, December 6, 2009

(101)---CONCEPT OF RISK UNDER ARBITRAGE PRICING MODEL

Concept of Risk under Arbitrage Pricing Model

The risk arising from the firm-specific factors is diversifiable. It is unsystematic risk. The risk arising from the market related factors cannot be diversified. This represents systematic risk. In capital asset pricing model, market risk primarily arises from the sensitivity of an assets returns to the market retains and this is reflected by the assets beta.

Just one factor the market retains affects the firms retain. Hence, capital asset pricing model is one factor model. The betas of the form would differ depending on their individual sensitivity to market. On the other hand Arbitrage pricing model assumes that market risk can be caused by economic factors such as changes in gross domestic product, inflation, and the structure of interest rates and these factors could affects firms differently.

For example; different firms may feel the impact of inflation differently. Therefore, under Arbitrage pricing model, multiple factors may be responsible for the expected return on the share of a firm. Therefore, under Arbitrage pricing model the sensitivity of the assets return to each factor is estimated. For each firm, there will be as many betas as the number of factors.

Saturday, December 5, 2009

(100)---CONCEPT OF RETURN UNDER ARBITRAGE PRICING THEORY

Concept of Return under Arbitrage Pricing Theory

In Arbitrage Pricing Theory, the return of an asset is assumed to have two components, predictable and unpredictable return.

The predictable or expected return depends on the information available to shareholders that a bearing on the share prices. The unpredictable or uncertain return arises from the future information. This information may be the firm specific and the market related macro economic factors.

The firm specific factors are special to the firm and affected only the firm. The market related factors affect all firms. Thus the uncertain return may come from the firm specific information and the market related information.

It is important to notice that the economy wide information may be future divided into the expected part and the unexpected or surprise part.

For example, the government may announce that inflation rate would be 5% next month. Since this information is already known, market would have already accounted for this and share prices would reflect it. After a month the government announces that the actual inflation rate was 6%. Share holders known now that the inflation is 1% higher than the anticipated rate. This is surprise news to them. The expected part of information influences the expected return while the surprise part affects the unexpected part or return.

Thursday, December 3, 2009

(99)---THE ARBITRAGE PRICING THEORY

The Arbitrage Pricing Theory

The capital asset pricing model is not always able to account for the difference is assets, returns using their betas. This paved way for the development of an alternative approach, called the arbitrage pricing theory, for estimating the assets “expected returns”.

Arbitrage pricing theory unlike capital asset pricing model, does not assume that investors employ mean variance analysis for their investment decisions. However, like capital asset pricing model, arbitrage pricing theory is found on the notion that investors are rewarded for assuming non diversifiable risk, diversifiable risk is not compensated beta is considered as the most important single factor in capital asset pricing model that captures the systematic risk of an asset.

In arbitrage pricing theory there are a number of industry specific and macro economic factors that affect the security returns. Thus a number of factors may measure the systematic risk of an asset under arbitrage pricing theory.

The fundamental logic of arbitrage pricing theory is that investors always indulge in arbitrage whenever they find differences in the returns of assets with similar risk characteristics.

Wednesday, December 2, 2009

(98)---LIMITATIONS OF CAPITAL ASSET PRICING MODEL

Limitations of Capital Asset Pricing Model

Capital asset pricing model has the following limitations,
  • It is based on unrealistic assumptions.
  • It id difficult to test the validity of Capital asset pricing model.
  • Betas do not remain stable over time.
Unrealistic assumptions
Capital asset pricing model is based on a number of assumptions that are far from the reality. For example it is very difficult to find a risk free security. A short term highly liquid government security is considered as a risk free security. It is unlikely that the government will default, but inflation causes uncertain about the real rate of return. The assumption of the equality of the lending and borrowing rates is also not correct. In practice these rates differ. Further investors may not hold highly diversified portfolios or the market indices may not well diversify. Under these circumstances capital asset pricing model may not accurately explain the investment behavior of investors and beta may fail to capture the risk of investment.
Difficult to validity
Most of assumptions may not be very critical for its practical validity. Therefore is the empirical validity of capital asset pricing model. Need to establish that the beta is able to measure the risk of a security and that there is a significant correlation between beta and the expected return. The empirical results have given mixed results. The earlier tests showed that there was a positive relation between returns and betas. However the relationship was not as strong as predicted by capital asset pricing model. Further these results revealed that returns were also related to other measures of risk, including the firm specific risk. In subsequent research some studies did not find any relationship between betas and returns. On the other hand other factors such as size and the market value and book value ratios were found as significantly related to returns.
All empirical studies testing capital asset pricing model have a conceptual problem. We need data on expected prices to test it. Unfortunately, in practice the researchers have to work with the actual past data. Thus this will introduce bias in the empirical results.
Betas do not remain stable over time
Stability of beta, beta is a measure of a securities future risk. But investors do not further data to estimate beta. What they have are past data about the share prices and the market portfolio. Thus, they can only estimate beta based on historical data. Investors can use historical beta as the measure of future risk only if it is stable over time. Most research has shown that the betas of individual securities are not stable over time. This implies that historical betas are poor indicators of the future risk of securities.
Capital asset pricing model is a useful device for understanding the risk return relationship in spite of its limitations. It provides a logical and quantitative approach for estimating risk. It is better than many alternative subjective methods of determining risk and risk premium. One major problem is that many times the risk of an asset is not captured by beta alone.