Financial risk manager frm part 1 of the frm exam covers the fundamental tools and techniques used in risk management and the theories that underlie their use standard capital asset pricing model we have learned in the previous lectures about the portfolio return and volatilities and about investors choices in holding efficient portfolios lying along the efficient frontier in this lecture we will learn about the market .
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At equilibrium that is we will derive pricing models for asset under equilibrium conditions in this lecture standard capital asset pricing model is discussed which will have a number of assumptions under ideal conditions in the next lecture we will see the effects of removing these assumptions agenda in the first model the markets will be assumed to be frictionless with various idealistic conditions we also plot the capital market line based under these .
Assumptions in the next lecture we will derive a model under more practical scenarios we will begin by explaining the assumptions underlying the standard model we will then study about the risk and its measures using bata finally we will learn about the security market line and how the price of acid changes with respect to the market market equilibrium let us first understand the concept of market equilibrium and equilibrium market conditions all .
Investors are assumed to hold efficient portfolios lying along the efficient frontier and have common return and risk expectations in such a case when all investors hold the same risky portfolio it must be market portfolio in other words and equilibrium investors hold the market portfolio various models have been developed to derive the price of the asset at equilibrium the standard form of capital asset pricing model CAPM is based on the most idealistic .
Condition let us now see those underlying assumptions assumptions the first assumption means that there is no transaction cost or any cost of purchasing or selling the security the second assumption means that you can buy or sell any asset infractions also the third assumption means that there are no income taxes and hence there is no difference in income from dividends or capital gains or profit from increase .
The price of security the fourth assumption means that single investors cannot manipulate or affect the market by buying or selling in huge amounts the fifth assumption means that the investors rely only on the return and volatility expectation in making an investment choice the sixth assumption means that investors can short sell the asset in any amount the seventh assumption implies that the investors can borrow and lend at the risk-free .
Rate to any amount the eighth assumption means that the expectations of investors are homogeneous or common the last assumption implies that all assets are marketable that is they can be sold and purchased at any time and in any quantity capital market line in the previous lecture we have plotted the efficient frontier as shown above we know that any investor will invest only in the efficient portfolio lying on the efficient frontier if the investor .
Allowed to borrow and lend at the risk-free rate then any portfolio will lie on the blue straight line this is also the case in practice as usually a portfolio is a combination of risky and risk free assets also as all investors have some expectations the nopal folio held by them at equilibrium must be the same which will be the market portfolio B M if the expected return of the market is our M and the standard deviation is Omega then the slope of this line is our .
M - RF over Omega and the equation is given by the are equal RF plus slope Omega where Omega is the standard deviation of the efficient portfolio this line is called the capital market line the equation signifies that the return increases by the amount of slope on increasing the risk that is standard deviation Omega by one unit hence the slope of the equation is the sensitivity of the portfolio return with .
Respect the risk taken by the investor high risk implies higher return along the capital market line now let us discuss the various types of risks and then we will introduce an important concept of beta of portfolio which is the measure of risk with respect to the market measures of risk you must have come across news of bankruptcy of some companies like Lehman Brothers if the investor only invested in one such company then his entire portfolio .
Risk therefore an investor usually diversifies his risk by investing in many securities so that the failure of one does not affect the overall portfolio this kind of company specific risk can thus be diversified away by holding many stocks as shown in the figure there is also another type of risk associated with the overall market such as the international recession affecting the world market such risk cannot be diversified away .
Investor has to bear this risk PETA measure of systemic risk the systematic risk or the market risk is denoted by the parameter beta it is the relative risk of the asset with the market that is the sensitivity of the asset with the market portfolio a higher beta implies greater sensitivity and hence a higher risk mathematically beta is equal to the covariance the asset with the market divided by the variance of the market portfolio .
Understand the implication of beta let's take an example suppose an asset has a beta of 1.5 this means that it is one and a half times more sensitive to the market portfolio if the market moves by say 20 percent upwards then the asset moves by 1.5 times this amount which is 30 percent similarly if the market falls by 10 percent then the asset will also fall by 15 percent it means the asset is one and a half times more sensitive than the market .
Movement a beta of one signifies market beta and the asset will move with the market a beta of less than one will be less sensitive to the market movement for example if the market moves by 30 percent and the asset has a beta of 0.5 then it will rise by fifteen percent in some rare cases you might come across negative beta that is the asset and market move in opposite direction
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