CAPM

The Capital Asset Pricing Model (CAPM) was introduced by Jack Treynor (1961,1962), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe, Markowitz and Merton Miller jointly received the Nobel Memorial Prize in Economics for this contribution to the field of financial economics. The model is based on the portfolio theory developed by Harry Markowitz. The model emphasises the risk factor in portfolio theory is a combination of two risk, systematic risk and unsystematic risk. The model suggest that a security's return is directly related to its systematic risk, which cannot be neutralised through diversification. The combination of both types of risk is called as total risk. The total variance of return is equal to market related variance of plus company's specific variance. CAPM explains the behaviour of security prices and provides a mechanism whereby investors could assess the impact of a proposed security in such a way that the risk premium or excess returns are proportional to systematic risk, which is indicated by the beta coefficient. The model is used for analysing the risk-return implications of holding securities. 
CAPM refers to the manner in which securities are valued in line with their anticipated risks and returns. A risk-averse investor prefers to invest in risk-free securities. For a small investor having few securities in his portfolio, the risk is greater. To reduce the unsystematic risk, he must build up well-diversified securities in his portfolio. 

Assumptions of CAPM
1. All assets in the world are traded.
2. All assets are infinitely divisible. 
3. There are only two periods of time in our world.
4. Security distributions are normal, or at least well described by two parameters. 
5. Preferences are well described by simple utility functions.
6. Everyone agrees on the inputs to the Mean-STD picture. 
7. All investors in the world collectively hold all assets. 
8. For every borrower, there is a lender. 
9. There is riskless security in the world.
10. All investors borrow and lend at the riskless rate. 

CAPM Graph, formula and calculations:-

Example:- Suppose an investment is twice as risky as investing in the stock market. The beta is 2, in this example. Suppose the stock market has yielded 11% return in the last fifty years, so the market rate of return is 11%. Suppose the Treasury note which matures in 10 years currently yields 6%, so the risk-free rate of return is 6%. 

Using CAPM, the discount rate r is calculated as follows:

r = 6% + 2 (11% - 6%) = 6% + 10% = 16%

So, 16% should be used as r in the NPV (net present value) calculations. 

Security market line

The SML essentially graphs the results from the capital asset pricing model (CAPM) formula. The x-axis represents the risk (beta), and the y-axis represents the expected return. The market risk premium is determined from the slope of the SML.

The relationship between β and required return is plotted on the securities market line (SML), which shows expected return as a function of β. The intercept is the nominal risk-free rate available for the market, while the slope is the market premium, E(Rm)− Rf. The securities market line can be regarded as representing a single-factor model of the asset price, where Beta is exposure to changes in value of the Market. The equation of the SML is thus:

It is a useful tool in determining if an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's expected return versus risk is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed.

Difference Between CML and SML

CML stands for Capital Market Line, and SML stands for Security Market Line.

The CML is a line that is used to show the rates of return, which depends on risk-free rates of return and levels of risk for a specific portfolio. SML, which is also called a Characteristic Line, is a graphical representation of the market’s risk and return at a given time.
One of the differences between CML and SML, is how the risk factors are measured. While standard deviation is the measure of risk for CML, Beta coefficient determines the risk factors of the SML.
The CML measures the risk through standard deviation, or through a total risk factor. On the other hand, the SML measures the risk through beta, which helps to find the security’s risk contribution for the portfolio.
While the Capital Market Line graphs define efficient portfolios, the Security Market Line graphs define both efficient and non-efficient portfolios.

While calculating the returns, the expected return of the portfolio for CML is shown along the Y- axis. On the contrary, for SML, the return of the securities is shown along the Y-axis. The standard deviation of the portfolio is shown along the X-axis for CML, whereas, the Beta of security is shown along the X-axis for SML.

Where the market portfolio and risk free assets are determined by the CML, all security factors are determined by the SML.
Unlike the Capital Market Line, the Security Market Line shows the expected returns of individual assets. The CML determines the risk or return for efficient portfolios, and the SML demonstrates the risk or return for individual stocks.

Well, the Capital Market Line is considered to be superior when measuring the risk factors.

Summary:

1. The CML is a line that is used to show the rates of return, which depends on risk-free rates of return and levels of risk for a specific portfolio. SML, which is also called a Characteristic Line, is a graphical representation of the market’s risk and return at a given time.

2. While standard deviation is the measure of risk in CML, Beta coefficient determines the risk factors of the SML.

3. While the Capital Market Line graphs define efficient portfolios, the Security Market Line graphs define both efficient and non-efficient portfolios.

4. The Capital Market Line is considered to be superior when measuring the risk factors.

5. Where the market portfolio and risk free assets are determined by the CML, all security factors are determined by the SML.

Empirical tests show market anomalies like the size and value effect that cannot be explained by the CAPM and is explained by Fama–French three-factor model

In asset pricing and portfolio management the Fama-French three factor model is a model designed by Eugene Fama and Kenneth French to describe stock returns. Fama and French were professors at the University of Chicago Booth School of Business.

The traditional asset pricing model, known formally as the Capital Asset Pricing Model, CAPM, uses only one variable, beta, to describe the returns of a portfolio or stock with the returns of the market as a whole. In contrast, the Fama–French model uses three variables. Fama and French started with the observation that two classes of stocks have tended to do better than the market as a whole: (i) small caps and (ii) stocks with a high book-to-market ratio (BtM, customarily called value stocks, contrasted with growth stocks). They then added two factors to CAPM to reflect a portfolio's exposure to these two classes:

Here r is the portfolio's expected rate of return,  is the risk-free return rate, and  is the return of the whole stock market. The "three factor"  is analogous to the classical  but not equal to it, since there are now two additional factors to do some of the work.  stands for "small (market capitalization) minus big" and  for "high (book-to-market ratio) minus low"; they measure the historic excess returns of small caps over big caps and of value stocks over growth stocks. These factors are calculated with combinations of portfolios composed by ranked stocks (BtM ranking, Cap ranking) and available historical market data. 

Moreover, once SMB and HML are defined, the corresponding coefficients  and  are determined by linear regressions and can take negative values as well as positive values. The Fama-French three factor model explains over 90% of the diversified portfolios returns, compared with the average 70% given by the CAPM. The signs of the coefficients suggested that small cap and value portfolios have higher expected returns—and arguably higher expected risk—than those of large cap and growth portfolios.

Options V/S Warrants

Introduction
 
Stock options and Stock warrants are two extremely popular derivative instruments that are traded in stock and derivative exchanges all over the world. 

Because stock options and warrants share the same leverage characteristics, they have been commonly assumed to be the same instrument called different names. Nothing is further from the truth. Even though stock options and stock warrants behave in almost the same fashion and can be traded in the same fashion, they are actually fundamentally different instruments. 

Even though a tiger roars like a lion roars, they are actually different animals with their own unique characteristics. Similarly, stock options and warrants have their own characteristics as well. 

In finance, a warrant is a security that entitles the holder to buy the underlying stock of the issuing company at a fixed exercise price until the expiry date.

Warrants and options are similar in that the two contractual financial instruments allow the holder special rights to buy securities. Both are discretionary and have expiration dates. The word warrant simply means to "endow with the right", which is only slightly different from the meaning of option. A warrant is like an option. It gives the holder the right but not the obligation to buy an underlying security at a certain price, quantity and future time. It is unlike an option in that a warrant is issued by a company, whereas an option is an instrument of the stock exchange. The security represented in the warrant (usually share equity) is delivered by the issuing company instead of by an investor holding the shares. 

Companies will often include warrants as part of a new-issue offering to entice investors into buying the new security. A warrant can also increase a shareholder's confidence in a stock, provided the underlying value of the security actually does increase over time.

There are two different types of warrants: a call warrant and a put warrant. A call warrant represents a specific number of shares that can be purchased from the issuer at a specific price, on or before a certain date. A put warrant represents a certain amount of equity that can be sold back to the issuer at a specified price, on or before a stated date. 

Differences on the basis of Contracting Parties 

Stock options are contracts between a person or institution owning a stock or willing to buy a stock and another person who either wants to buy or sell those stocks at a specific price. In this aspect, stock options are just like the option you sign when you buy a house from a seller of that house. It's a contract between a party who owned the stock through purchase from the open market and another party who wish to buy that stock from the writer of the options contract. It is essentially a contract between two investors. In this aspect, a Market Maker is an investor as well because they too accumulate those stocks and options from the open market. 

Stock Warrants on the other hand are contracts between investors and the bank or financial institution issuing those warrants on behalf of the company whose stocks the warrants are based on. When you buy warrants, it is these financial institutions selling it to you and when you sell warrants, it is these same financial institutions buying from you and not another investor. Companies issuing warrants do so in order to encourage the sale of their shares and to hedge against a reduction in company value due to a drop in their company share price. Therefore, when you buy a warrant, you are helping the company issuing it no matter if it gets exercised or not. However, in a stock option transaction, the company itself does not receive a direct benefit at all. It is the winning investor who enjoys the profits. The issuing bank or financial institution also acts as market makers for the warrants that they issue, hence there are no third party market makers like those making markets for stock options. 

Warrants are transferable, quoted certificates, and they tend to be more attractive for medium-term to long-term investment schemes. Tending to be high-risk, high-return investment tools that remain largely unexploited in investment strategies, warrants are also an attractive option for speculators and hedgers. Transparency is high and warrants offer a viable option for private investors as well. This is because the cost of a warrant is commonly low, and the initial investment needed to command a large amount of equity is actually quite small. 

Advantages 
Let us look at an example that illustrates one of the potential benefits of warrants. Say that ABC shares are currently priced on the market for Rs. 15 per share. In order to purchase 1,000 shares, an investor would need Rs. 1,5000. However, if the investor opted to buy a warrant (representing one share) that was going for Rs. 5 per warrant, he or she would be in possession of 3,000 shares using the same Rs. 1,5000. 

Because the prices of warrants are low, the leverage and gearing they offer is high. This means that there is a potential for larger capital gains and losses. While it is common for both a share price and a warrant price to move in parallel (in absolute terms) the percentage gain (or loss), will be significantly varied because of the initial difference in price. Warrants generally exaggerate share price movements in terms of percentage change. 

Let us look at another example to illustrate these points. Say that share ABC gains Rs. 5 per share from 15, to close at Rs 20. The percentage gain would be 33.33%. However, with a  gain in the warrant, from Rs. 5 to 10, the percentage gain would be 100%. 

In this example, the gearing factor is calculated by dividing the original share price by the original warrant price: 15 / 5 = 3. The "3" is the gearing factor - essentially the amount of financial leverage the warrant offers. The higher the number, the larger the potential for capital gains (or losses). 

Warrants can offer significant gains to an investor during a bull market. They can also offer some protection to an investor during a bear market. This is because as the price of an underlying share begins to drop, the warrant may not realize as much loss because the price, in relation to the actual share, is already low.

Differences on the basis of Customizability of Terms of Issue

Standardized stock options all around the world are issued with a fixed structure and framework with a common method of calculation, standardized policy of strike difference, standardized contract size and standardized terms of exercise / delivery. All these rules are set by the individual exchanges so that all participants may "play this game" on equal terms. This standardization is necessary as stock options are contracts between individual investors who may not be professional financial institutions. 

Warrants, however, are highly customizable as the issuer crafts the terms of each new issue according to their needs at that point in time. The most significant of these customizable terms is what is known as the "conversion ratio" or "cover ratio". Conversion ratio is simply the number of stocks that are represented with each warrant contract. This conversion ratio varies with each warrant contract unlike the fixed contract size in stock options. In fact, each warrant contract may even convert to just a fraction of the underlying share rather than the 100 or 1000 shares in stock options. The life span of warrants are also commonly much longer than options as the issuers are free to decide on an expiration date that could go as far as 15 years in some countries. A warrant's lifetime is measured in years (as long as 15 years), while options are typically measured in months. Even LEAPS (long-term equity anticipation securities), the longest stock options available, tend to expire in two or three years. Upon expiration, the warrants are worthless unless the price of the common stock is greater than the exercise price.

Differences on the basis of Shorting

Because stock options are contracts between individual investors, anyone could produce a new option and throw it for sale into the market by "shorting" or "writing" using a Sell To Open order. Warrants, on the other hand, are issued by the issuing bank or financial institution only, hence they cannot be shorted. 

Differences on the basis of Exercise & Delivery
 
Both Warrants and Stock options are either American, allowing the investor to exercise at any time during the life of the options, or European style, allowing the investor to exercise only during expiration. Warrants issued by the company itself are dilutive. When the warrant issued by the company is exercised, the company issues new shares of stock, so the number of outstanding shares increases. When a call option is exercised, the owner of the call option receives an existing share from an assigned call writer (except in the case of employee stock options, where new shares are created and issued by the company upon exercise). Unlike common stock shares outstanding, warrants do not have voting rights.Remember, the issuers of warrants are the issuing banks directly representing the companies issuing the shares. These companies win as long as their shares get sold and capital raised. This is unlike stock options where the investor selling the options could lose significant amount of money when call options they wrote gets in the money and then subsequently exercised. 

Differences on the basis of Trading Strategies

As stock options can be bought or shorted, there are a myriad of hedging and trading strategies that can be used, including credit strategies. As stock warrants can only be bought, it can only be traded like stocks without the flexibility and versatility that stock options can offer.

Conclusion
 
Even though Warrants share the same trading characteristics of Stock Options, it is really a totally unique trading instrument. Warrants are created more like over-the-counter exotic options where the terms of each warrant is highly customizable to meet the needs of the issuer and then securitized and publicly traded. In fact, the very same warrants that are publicly traded in derivatives exchange are traded in over-the-counter markets (OTC) as well, while in the US, only non-standardized options are traded OTC. In short, warrants are a form of exotic option that are capable of being traded publicly. 

Here is a list of main differences between Stock Warrants and Stock Options. 

	Stock Warrants	Stock Options
Contract Terms	Defined by issuer	Standardized by exchange
Trading	Cannot be freely shorted	Can be shorted
Strike Prices	Only those issued	Usually a lot more strike prices and expiration
Delivery	Delivered by issuer	Delivered by investors

Due to these differences, especially the fact that warrants cannot be freely shorted, the hedging possibilities as well as the kinds of options strateiges that can be executed using warrants are a lot lesser than stock options. In fact, the only hedging strategies one can execute with warrants is the Protective Put strategy and delta neutral hedging using put warrants, which acts in almost the exact fashion as a put option. 

So far, because Warrants can only be bought and not shorted, it is mainly used by speculators as a form of stock replacement. 

A Bittersweet Stock Jump 

One notable instance in which warrants made a big difference to the company and investors took place in the early 1980s when the Chrysler Corporation received governmentally guaranteed loans totaling approximately $1.2 billion. Chrysler used warrants - 14.4 million of them - to "sweeten" the deal for the government and solidify the loans. 

Because these loans would keep the auto giant from bankruptcy, management showed little hesitation issuing what they thought was a purely superficial bonus that would never be cashed in. At the time of issuance Chrysler stock was hovering around $5, so issuing warrants with an exercise price of $13 did not seem like a bad idea. However, the warrants ended up costing Chrysler approximately $311 million, as their stock shot up to nearly $30. For the federal government, this "cherry on top" turned quite profitable, but for Chrysler it was an expensive afterthought.