UNIT II

Valuation of Financial Securities, Instruments & Derivatives

Securities Valuation means determining the market value of equity instruments (viz. common stock and preferred stock), debt instruments (viz. bonds and bills of exchange), derivatives (viz. options and futures) issued by government agencies, financial institutions and corporate organizations.

The main factors driving the securities market value include liquidity, demand and supply of similar instruments, stock market rates of similar securities, present value of future cash flows etc

Debenture Valuation: A bond is an instrument of debt issued by a business house or a government unit. The bonds may be issued at par, premium or discount. The par value is the amount stated on the face of the bond. It states the amount the firm borrows and promises to repay at the time of maturity.

The bonds carry a fixed rate of interest payable at fixed intervals of time. The interest is calculated by multiplying the value of bonds with the rate of interest.

Bond valuation is, generally, called debt valuation because the features that distinguish bonds from other debts are primarily non-financial in nature. Since bonds have a promised payment stream, they are less risky as compared to the shares. But it does not mean that they are totally risk free.

Therefore, the required rate of return on a firm’s bond will exceed the risk free interest rate but will be less than the required rate of return on shares. The differences in required rates of return among bonds of different companies are caused by differences in ‘default risk’. The value of the bond depends upon the discount rate. It will decrease with every increase in the discount rate.

For the purpose of valuation, bonds may be classified into two categories: (i) Bonds with a maturity period, and When the bonds have a definite maturity period, its valuation is determined by considering the annual interest payments plus its maturity value.

(ii) Bonds in Perpetuity: Perpetuity bonds are the bonds which never mature or have infinitive maturity period. Value of such bonds is simply the discounted value of infinite streams of interest (cash) flows.

Meaning of Security Valuation: Security valuation is important to decide on the portfolio of an investor. All investment decisions are to be made on a scientific analysis of the right price of a share. Hence, an understanding of the valuation of securities is essential. Investors should buy underpriced shares and sell overpriced shares. Share pricing is thus an important aspect of trading. Conceptually, four types of valuation models are discernible. They are:

(i) Book value,

(ii) Liquidating value,

(iii) Intrinsic value,

(iv) Replacement value as compared to market price.

(i) Book Value: Book value of a security is an accounting concept. The book value of an equity share is equal to the net worth of the firm divided by the number of equity shares, where the net worth is equal to equity capital plus free reserves. The market value may fluctuate around the book value but may be higher if the future prospects are good.

(ii) Liquidating Value (Breakdown Value): If the assets are valued at their breakdown value in the market and take net fixed assets plus current assets minus current liabilities as if the company is liquidated, then divide this by the number of shares, the resultant value is the liquidating value per share. This is also an accounting concept. (iii) Intrinsic Value: Market value of a security is the price at which the security is traded in the market and it is generally hovering around its intrinsic value. There are different schools of thought regarding the relationship of intrinsic value to the market price. Market prices are those which rule in the market, resulting from the demand and supply forces. Intrinsic price is the true value of the share, which depends on its earning capacity and its true worth. According to the fundamentalist approach to security valuation, the value of the security must be equal to the discounted value of the future income stream. The investor buys the securities when the market price is below this value.

Thus, for fundamentalists, earnings and dividends are the essential ingredients in determining the market value of a security. The discount rate used in such present value calculations is known as the required rate or return. Using this discount rate all future earnings are discounted back to the present to determine the intrinsic value.

CAPITAL ASSET PRICING MODEL (CAPM)

In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.

Capital Asset Pricing Model - CAPM

The capital asset pricing model is a model that describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for the pricing of risky securities, generating expected returns for assets given the risk of those assets and calculating costs of capital.

In finance, one of the most important things to remember is that return is a function of risk. This means that the more risk you take, the higher your potential return should be to offset your increased chance for loss.

One tool that finance professionals use to calculate the return that an investment should bring is the Capital Asset Pricing Model which we will refer to as CAPM for this lesson. CAPM calculates a required return based on a risk measurement. To do this, the model relies on a risk multiplier called the beta coefficient, which we will discuss later in this lesson. Like all financial models, the CAPM depends on certain assumptions. Originally there were nine assumptions, although more recent work in financial theory has relaxed these rules somewhat. The original assumptions were:

1. Investors are wealth maximizers who select investments based on expected return and standard deviation. 2. Investors can borrow or lend unlimited amounts at a risk-free (or zero risk) rate. 3. There are no restrictions on short sales (selling securities that you don't yet own) of any financial asset. 4. All investors have the same expectations related to the market. 5. All financial assets are fully divisible (you can buy and sell as much or as little as you like) and can be sold at any time at the market price. 6. There are no transaction costs. 7. There are no taxes. 8. No investor's activities can influence market prices. 9. The quantities of all financial assets are given and fixed.

Obviously, some of these assumptions are not valid in the real world (most notably no transaction costs or taxes), but CAPM still works well, and results can be adjusted to overcome some of these assumptions.

The capital asset pricing model (CAPM) is a widely-used finance theory that establishes a linear relationship between the required return on an investment and risk. The model is based on the relationship between an asset's beta, the risk-free rate (typically the Treasury bill rate) and the equity risk premium (expected return on the market minus the risk-free rate).

At the heart of the model are its underlying assumptions, which many criticize as being unrealistic and might provide the basis for some of the major drawbacks of the model.

Drawbacks

Like many scientific models, the CAPM has its drawbacks. The primary drawbacks are reflected in the model's inputs and assumptions. • Risk-free Rate (Rf): The commonly accepted rate used as the Rf is the yield on short- term government securities. The issue with using this input is that the yield changes daily, creating volatility.

• Return on the Market (Rm): The return on the market can be described as the sum of the capital gains and dividends for the market. A problem arises when at any given time, the market return can be negative. As a result, a long-term market return is utilized to smooth the return. Another issue is that these returns are backward-looking and may not be representative of future market returns. • Ability to Borrow at a Risk-free Rate: CAPM is built on four major assumptions, including one that reflects an unrealistic real-world picture. This assumption, that investors can borrow and lend at a risk-free rate, is unattainable in reality. Individual investors are unable to borrow (or lend) at the same rate as the US government. Therefore, the minimum required return line might actually be less steep (provide a lower return) than the model calculates. • Determination of Project Proxy Beta: Businesses that use CAPM to assess an investment need to find a beta reflective to the project or investment; often a proxy beta is necessary. However, accurately determining one to properly assess the project is difficult and can affect the reliability of the outcome.

Advantages

Despite the aforementioned drawbacks, there are numerous advantages to the application of CAPM.

• Ease-of-use: CAPM is a simplistic calculation that can be easily stress-tested to derive a range of possible outcomes to provide confidence around the required rates of return. • Diversified Portfolio: The assumption that investors hold a diversified portfolio, similar to the market portfolio, eliminates unsystematic (specific) risk. • Systematic Risk (beta): CAPM takes into account systematic risk, which is left out of other return models, such as the dividend discount model (DDM). Systematic or market risk is an important variable because it is unforeseen and often cannot be completely mitigated because it is often not fully expected. (See: Systematic And Unsystematic Risk). • Business and Financial Risk Variability: When businesses investigate opportunities, if the business mix and financing differ from the current business, then other required return calculations, like the weighted average cost of capital (WACC), cannot be used. However, CAPM can

Arbitrage Pricing Theory - APT

Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset's returns can be predicted using the linear relationship between the asset’s expected return and a number of macroeconomic variables that capture systematic risk. It is a useful tool for analyzing portfolios from a value investing perspective, in order to identify securities that may be temporarily mispriced.

Arbitrage Pricing Theory

Arbitrage Pricing Theory (APT) is an alternate version of Capital Asset Pricing Model (CAPM). This theory, like CAPM provides investors with estimated required rate of return on risky securities. APT considers risk premium basis specified set of factors in addition to the correlation of the price of the asset with expected excess return on the market portfolio. As per assumptions under Arbitrage Pricing Theory, return on an asset is dependent on various macro-economic factors like inflation, exchange rates, market indices, production measures, market sentiments, changes in interest rates, movement of yield curves etc.

The Arbitrage pricing theory based model aims to do away with the limitations of one-factor model (CAPM) that different stocks will have different sensitivities to different market factors which may be totally different from any other stock under observation. In layman terms, one can say that not all stocks can be assumed to react to single and same parameter always and hence the need to take multifactor and their sensitivities.

Calculating Expected Rate of Return of an Asset Using Arbitrage Pricing Theory (APT) Arbitrage Pricing Theory Formula – E(x) = rf + b1 * (factor 1) +b2 *(factor 2) + ….+ bn *(factor n) Where,

E(X) = Expected rate of return on the risky asset Rf = Risk-free interest rate or the interest rate that is expected from a risk-free asset (Most commonly used in U.S. Treasury bills for U.S.)

B = Sensitivity of the stock with respect to the factor; also referred to as beta factor 1, 2 … N = Risk premium associated with respective factor As the formula shows, the expected return on the asset/stock is a form of linear regression taking into consideration many factors that can affect the price of the asset and the degree to which it can affect it i.e. the asset’s sensitivity to those factors.

If one is able to identify a single factor which singly affects the price, the CAPM model shall be sufficient. If there are more than one factor affecting the price of the asset/stock, one will have to work with a two-factor model or a multi-factor model depending on the number of factors that affect the stock price movement for the company.

To understand APT, it is important for us to learn the underlying assumptions of this theory as given below

ARBITRAGE PRICING THEORY ASSUMPTIONS ▪ The theory is based on the principle of capital market efficiency and hence assumes all market participants trade with the intention of profit maximisation ▪ It assumes no arbitrage exists and if it occurs participants will engage to benefit out of it and bring back the market to equilibrium levels. ▪ It assumes markets are frictionless, i.e. there are no transaction costs, no taxes, short selling is possible and an infinite number of securities is available. Let us now look at some arbitrage pricing theory advantages and disadvantages summarized as under:

ARBITRAGE PRICING THEORY BENEFITS ▪ APT model is a multi-factor model. So, the expected return is calculated taking into account various factors and their sensitivities that might affect the stock price movement. Thus, it allows selection of factors that affect the stock price largely and specifically. ▪ APT model is based on arbitrage free pricing or market equilibrium assumptions which to a certain extent result in a fair expectation of the rate of return on the risky asset. ▪ APT based multi-factor model places emphasis on the covariance between asset returns and exogenous factors, unlike CAPM. CAPM places emphasis on the covariance between asset returns and endogenous factors. ▪ APT model works better in multi-period cases as against CAPM which is suitable for single period cases only. ▪ APT can be applied to the cost of capital and capital budgeting decisions. ▪ The APT model does not require any assumption about the empirical distribution of the asset returns, unlike CAPM which assumes that stock returns follow a normal distribution and thus APT a less restrictive model. ARBITRAGE PRICING THEORY LIMITATIONS ▪ The model requires short listing of factors that impact the stock under consideration. Finding and listing all factors can be a difficult task and runs a risk of some or the other factor being ignored. Also, the risk of accidental correlations may exist which may cause a factor to become substantial impact provider or vice versa. ▪ The expected returns for each of these factors will have to be arrived at, which depending on the nature of the factor, may or may not be easily available always. ▪ The model requires calculating sensitivities of each factor which again can be an arduous task and may not be practically feasible. ▪ The factors that affect the stock price for a particular stock may change over a period of time. Moreover, the sensitivities associated may also undergo shifts which need to be continuously monitored making it very difficult to calculate and maintain.