75. Arbitrage Pricing Theory (apt). Capital Asset Pricing Model (capm). Теория арбитражного ценообразования. Модель оценки капитальных активов.

CAPM is a model for pricing an individual security or portfolio. For individual securities, we make use of the security market line (SML) and its relation to expected return and systematic risk (β) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio: (E(R_i)-R_f)/β_i =E(R_m)-R_f, where E(R_i)-R_f is risk premium; E(R_m)-R_f is market premium; β_i=Cov(R_i,R_m)/Var(R_m) - implied risk.

The general idea is that investors need to be compensated in two ways: time value of money and risk premium. The time value of money is represented by the risk-free (r_f) rate and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. (E(R_i)=R_f+β_i*(E(R_m)-R_f))

The risk of a portfolio comprises systematic risk and unsystematic risk. Systematic risk refers to market risk. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio. The same is not possible for systematic risk within one market.

Assumptions: 1) Perfect market; 2) Divisible into parts securities; 3) No transaction costs and taxes; 4) Can lend and borrow unlimited amounts under the risk free rate of interest.

Application: helps to determine the return on securities and identify those with return>required rate of return to invest.

APT is a general theory of asset pricing which contends that a relationship between the returns of a portfolio and the returns of a single asset may be charted through a linear combination of many independent macroeconomic variables. These macroeconomic variables are called risk factors. In other words, APT asserts that if two or more securities or portfolios have identical return and risk, then they should sell for one price. Since, APT gives the expected return of an asset, arbitrageurs use it to identify and take advantage from mispriced securities. With the help of APT, it is possible to look for arbitrage opportunities with higher return and lower risk (beta).

Assumptions: 1) expectations are homogeneous 2) market is open to frictionless arbitrage.

APT gives the expected return on asset i as E(R_i)=R_f+β₁*(E(R₁)-R_f)+β₂*(E(R₂)-R_f)+ +…+β_n*(E(R_n)-R_f)+e_i,where: R_f = risk free interest rate, e_i = random return, β_i = sensitivity of the asset to factor i, E(R_i) - R_f) = risk premium associated with factor i, where i = 1, 2,...n.

Few macroeconomic factors tend to influence the price of the security are a.) Change in GDP or industrial production; b.) Surprises in inflation (deflation); c.) Shifts in the Yield Curve.

APT seeks to overcome the weaknesses of CAPM as it uses fewer assumptions. While the CAPM formula requires the market's expected return, APT uses the risky asset's expected return and the risk premium of a number of macro-economic factors.

76. Valuation Models Based on Price Multiples: P/E, P/BV, P/S. Ценовые множители и модели оценки на их основе. (Самый бессмысленный вопрос, который я когда-либо видел!)

In simple words, multiples are ratios of any company (P/E, P/Sales, etc.) If an investor wants to invest money, for example, into shares, he will need to determine the shares of which company to purchase. So, he needs to conduct fundamental analysis to understand the financial situation in different potential objects of investment and compare results. The simplest way to do this is to compare financial ratios and invest into the company, where the ratios indicate the best results from the investment attractiveness point of view. Price multiples are ratios, where share price is in nominator and shows the relative relationship of share price to earnings, gross sales, etc.

To make the comparison between assets (securities) in which to invest, we should identify the comparable ones or peer group. A peer group is a set of companies or assets which are selected as being sufficiently comparable to the company or assets being valued (usually by virtue of being in the same industry or by having similar characteristics in terms of earnings growth and/or return on investment). In practice, no two businesses are alike, and analysts will often make adjustment to the observed multiples in order to attempt to harmonize the data into more comparable format. These adjustments may be based on a number of factors, including: business model, industry, geography, seasonality, capital structure, size, etc.

Momentum indicators relate either price or a fundamental (such as earnings) to the time series of their own past values, or in some cases to their expected value. The method of comparables involves using a price multiple to evaluate whether an asset is relatively fairly valued, relatively undervalued, or relatively overvalued in relation to a benchmark value of the multiple.

When the peer group consists of public quoted companies, it is called comparable company analysis. When the peer group consists of companies or assets that have been acquired in mergers or acquisitions, it is called precedent transaction analysis.

Multiple	Definition	Advantages	Disadvantages
P/E ratio	1)Share price / Earnings per share (EPS);	1)Most commonly used equity multiple. 2)Data availability is high.	1)EPS can be subject to differences in accounting policies and manipulation; 2)Unless adjusted, can be subject to one-off exceptional items; 3)Cannot be used if earnings are negative.
Price / book ratio	Share price / book value per share	1)Can be useful where assets are a core driver of earnings such as capital-intensive industries; 2) Most widely used in valuing financial companies, such as banks, which rely on a large asset base to generate profits.	1)Book values for tangible assets are stated at historical cost, which is not a reliable indicator of economic value; 2) Book value for tangible assets can be significantly impacted by differences in accounting policies.
Price / Sales	Share price / sales per share	1)Easy to calculate; 2)Can be applied to loss making firms; 3)Less susceptible to accounting differences than other measures.	1)Mismatch between nominator and denominator in formula (EV/Sales is a more appropriate measure); 2)Not used except in very broad, quick approximations.

On the basis of forecasted future net income, discount factor and historical average ratio, it is possible to value future share price and, thus, value the benefits an investor will enjoy if invests.