Lecture 07

[Music] introduction to risk and return till now we have gone through different topics without discussing the concept of risk but we need to take this term risk headon now we'll no longer be satisfied with a slightly vague statement that is the opportunity cost of capital depends on the risk of the project we need to understand how risk is defined and how to compute risk we start the discussion by understanding the basics of risk written framework the basics of risk written framework is explained by comparing these very different instrument that is tbls government bonds and common stock then we discuss the empirical estimation of risk some of the very important measures of risk that we discuss are variance and standard deviation then we discuss the concept of risk diversity ification in the context of portfolios we discuss and understand the risk written computation for a two security case and extend the frame to a multi-city case we find that the risk of any security comprise two components first stock specific diversifiable risk component and second Market risk or systematic risk component the stock specific osm critic risk can be Diversified by simply adding more Securities in the portfolio the market risk of a portfolio cannot be Diversified away and therefore becomes the Bedrock of risk for a well Diversified portfolio next we discuss the contribution of a security to a portfolio and how to empirically estimate the same we discussed the concept of beta that is the sensitivity of a security to Market movements lastly we discussed the concept of value additivity that is the sum of present values of cash flows for different project assets is same whether considered individually or taken together as a unit in a firm basics of risk return framework in this video we'll discuss the basics of risk return framework by comparing the performance of three broad instruments that is treasury bills government bonds and common stock we'll also discuss the concept of risk premium and the factors that affect this risk premium consider three broad instrument categories that is treasury bills government bonds and common stock these Investments offer different degrees of risk first consider treasury bills these are short maturity instruments with no risk of default that is one can obtain a sure short payoff for small periods for example 3 months by investing in these instruments although there is a still uncertainty due to inflation the actual real value may also depend upon the prevailing inflation rates compare this to long-term government bonds this is a long-term instrument and fluctuates a lot with interest rates bond prices fall when interest rates rise and bond prices rise when interest rates fall next we have common stocks that is Market portfolios like nifty 50 or S&P 500 Common Stocks do not have a finite maturity the investor in common stock shares the ups and downs of the issuing company consider the performance of these three instruments that is treasury bills government bonds and commer stocks for the us over 100 years as shown in the figure here that is $1 investment at the beginning of 1900 and its value by 2008 assuming all the dividends and interest payments are reinvested in the same asset portfolios the values shown here are nominal and do not account for the inflation observe the investment performance of different instruments in the figure shown here it appears that performance of these instruments match with their risk order a dollar invested in treasury bills would have grown to $71 by the end of 2008 that is a nominal return of 4% a $1 investment in long-term bonds would have become $242 a nominal return of 5.5% investors who placed $1 in Common Stocks would have received $1,276 a nominal return of 11.1% it seems that the Common Stocks provided the highest returns over this period one important point to be noted here returns from common stock fluctuate a lot therefore averages over short period are not so many meaningful notice the difference between the Returns on treasury bills and Common Stocks this additional return of 11.1 minus 4% equal to 7.1% this additional return can also be said to be the risk premium received by investors that is additional returns for bearing the risk associated with their investment in stocks for example on a given year treasury bill rate was 0.2% and you are asked to estimate the expected return on Common Stocks a reasonable estimate would be obtained by adding this 7.1% to obtain the total return of 7.3% however this assumes that there is a stable risk premium on the common stock portfolio that is future risk premium can be measured by the average P risk premium however is it fair to say that the returns investors were demanding for bearing a given amount of risk 50 years ago they are demanding the same returns for the amount of risk today as well the there can be various reasons to argue against it first economic and financial conditions change over time therefore risk perceptions also change and depend upon the current market conditions investors risk tolerance and risk expectations also change over time for example it is often considered that dividend deals are a good proxy to measure this risk premium when investors have a higher risk tolerance they are content with a lower return and a lower dividend yield is observed in contrast when risk tolerance is low investors demand the higher return for the same levels of risk and the higher dividend yield is observed let us put some numbers here consider a stock bid $12 dividend expected by the end of the year investors are expecting a 10% return on this stock present value of this stock can be easily computed as shown here present value PV equal to Dividend 1 upon Rus G = to 12 upon 0 1- 0.07 equal to $400 here dividend yield is 12 upon 400 equal to 3% imagine that now investors revise their expectations and expect a dividend yield of 12% and demand an expected return of 9% the revised price estimate can be computed as shown here present value PV equal to 12 upon 0.09 minus 0.07 equal to $600 thus a fall from 10% to 9% in the required returns leads to a 550% rise in the stock price this is one case where the returns required by investors have come down if we would have relied on past returns then we would have overestimated the risk premium desired by the investors today if markets are liquid and efficient and the stock are fairly priced then the following relationship holds nicely that is r equal to div 1 upon P plus G that is expected Returns on the stock reflect the dividend y and the growth rate of dividends here R minus RF is the risk premium expected here RF equal to risk free rate this risk premium is expected and may be different from the actual realized risk premium there can be many reasons this risk premium varies over time investors are overly optimistic in some years and pessimistic in others about G that is expected dividend growth rates in future the second component is dividend deal that is div 1 upon p prior literature suggests that this dividend deal is often less correlated with the dividend growth rates G it is considered that this dividend deal is related to risk premium however historical yields may not provide a good estimate of risk premium in future therefore one needs to have a more efficient and contemporaneous measure of risk to summarize in this video we compared the performance of three Securities with different risks that is treasury bills government bonds and common stock we observed that these instruments offer different returns that are aligned to their risk for now we approximated the risk with the fluctuations observed in the instrument this excess return for bearing additional risk is often referred to as the risk premium of the instrument this risk premium varies over time and depends upon a number of factors these include prevailing economic and financial conditions investor taste risk preferences among others we also discussed that variation in dividend yield is one such measure of risk premium measures of risk in this video we'll discuss the empirical estimation of variance or standard deviation as a measure of risk a very prominent statistical measure of risk is variance or standard deviation but simply variance of return is the expected Square deviation from the expected returns as shown here that is variance of RT equal to expected value of RT minus r bar whole squ where RT is the actual return and r bar is the expected returns standard deviation is simply the square root of variance that is standard deviation SD equal to variance of RT square root of whole standard deviation is often denoted by the symbol Sigma and variance by Sigma Square let us understand this concept with a simple coin tossing game the following probabilities are observed first head plus head gain of 40% head plus tail gain of 10% tail plus head gain of 10% and tail plus tail loss of 20% thus there is a 25% chance that your return will be 40% 50% chance that your return will be 10% and 25% chance that you lose 20% the overall expected return from this exercise can be easily computed as shown here R Bar that is expected returns equal to 0.25 into 40% + 0.5 into 10% + 0.25 into - 20% = to 10% now let us compute the variance and standard deviation of these returns as shown in the table here variance equal to 225 + 225 = 450 and standard deviation that is Sigma = toare < TK of 450 = 21% please note that standard deviation can be expressed in percentages thus we have now computed the standard deviation of this game as 21% how do we understand this standard deviation of variance financially this variance is a measure of risk an event is considered to be risky if there are many possibilities or outcomes associated with it as these outcomes or possibilities increase that is the spread of possible outcomes increases the event is said to have become riskier standard or variance is a summary measure of these possibilities that is spread in the possible outcome for example if there was one shortshot outcome of our coin tossing game that is one single possibility whether positive or negative we would have said that there's no risk with this event thus one way to define risk is that there are various possible outcomes in an event and in a similar manner the risk of an asset can be completely expressed by writing all the possible outcomes and the possible payoffs associated with each out outcome these outcomes are summarized using variance or standard deviation measure if the outcome was certain that is no risk then the standard deviation would have become zero the positive value associated with the standard measure precisely indicates this uncertainty one of the challenges in performing such computations is the estimation of probability associated with each outcome one way to go about this is to observe past variable it is assumed that those Securities or portfolios that have shown High variability will also be more volatile in future for example consider the historical volatilities of three different kinds of Securities as observed over the period 1900 to 2008 as shown here in the table treasury bills 2.8% standard deviation govern bonds 88.3% standard deviation Common Stocks 20.2% standard deviation it appears that t are the least variable and Common Stocks are the most variable there is no reason to believe that this variability will remain the same in future still though it is an important indicator for example there'll be periods of excessively High volatility such as 2008 financial crisis at the peak of crisis in 2008 October November the standard deviation was 70% per enom the risk premium increases during these times of volatile periods and comes to down during normaly to summarize in this video we discussed the computation of standard deviation or variance as a measure of risk any event with more than one output is considered as a risky event We examined this with the help of a single simple coin tossing game however one needs to assign the probabilities in order to estimate the standard deviation historically empirically observed values for example pass returns are often employed for this purpose diversification of risk in this video we'll discuss the concept of diversification with the help of portfolios we'll also discuss the concept of specific risk and Market risk one can compute the measure of variability for individual Securities as well as the portfolio of Securities the standard deviation of selected us Common Stocks for the period 2004 to 2008 such as Amazon at 50.9% Ford at 47.2% Newmont at 36.1% Dell at 30.9% and Starbucks at 30.3% was much less than the standard deviation of Market portfolio that is 13% during this period Market portfolio is a collection of many stocks in the form of indices such as S&P 500 or nifty50 it is well known that individual stocks are more volatile than market indices this raises an important question the market portfolio is made up of individual stock stocks so the variability of Market doesn't reflect or as same as the variability of individual stock components the simple answer to this question is that diversification reduces variability consider the figure shown here it shows the change in standard deviation of the portfolio as the number of stocks are increased notice how portfolio standard deviation or risk decreases as one two three and more stocks are added average risk that is the standard deviation of portfolio decreases as the number of stocks in the portfolio are increased this is called diversification please note that diversification reduces risk rapidly at first and then the process is more gradual we can see that even with an addition of small number of stocks one can cut the portfolio variability by almost half this concept of diversification raises because stocks do not move exactly together this is so because stock prices are not perfectly correlated consider another example where two stocks Dell and Starbucks and the 50/50 portfolio of these stocks is plotted over time assume an initial investment of $100 it is very easy to see here that diversification provides a substantial reduction in variability the standard deviation of both of these stocks was about 30% however these stocks did not move in a lock step manner the decline of one stock was often compensated by the rise of other therefore the standard deviation of the 50/50 portfolio of these stocks was about 20% per year the risk that can be eliminated by diversification is called specific risk the specific risk arises due to issues that are predominantly specific to the company or its close players there's another category of risk called Market risk that cannot be Diversified Market risk arises due to the factors that are affecting the entire economy and the market in a similar manner this risk causes Securities in a market to move together all in centry thus Market risk affects security movements in a similar manner up or down and therefore cannot be Diversified away through addition of more Securities in the portfolio this division between Market risk and specific risk is shown here in the figure it can be seen that if you have a single stock the specific risk is very important but if you have a portfolio of 20 or more stocks Market risk becomes more important that is for a reasonably well Diversified portfolio only Market risk matters that is the predominant source of risk for such a diversified portfolio is the movement of Market whether it will rise or fall taking the portfolio with it to summarize in this video we discussed the concept of diversification individual Securities do not move in a lock step manner therefore adding more Securities to a portfolio leads to diversification this diversification reduces the stock specific component of the risk however the market risk cannot be Diversified away this is so because Market risk affects most of the Securities in a market in a similar manner Computing portfolio risk in this video we discussed the competation of risk and return for a portfolio of multiple stocks we build the concept with a two stock portfolio and extend the argument for a portfolio of multiple Securities we mathematically show how for a well Diversified portfolio comprising a large number of stocks the stock specific risk is eliminated and only Market risk remains relevant we now know that diversification reduces the risk of a portfolio to develop this understanding we need to know how the risk of a portfolio depends on the risk of individual shares consider a portfolio of stocks comprising stock a with 60% weight and Stock B 40% weight also assume that a has expected returns of 3.1% and B has expected returns of 99.5% the expected Returns on this portfolio can be easily computed as shown here expected portfolio return equal to 0.60 into 3.1 + 0.40 into 9.5 = to 5.7% calculating the expected returns is very intuitive and easily done however Computing the risk of the portfolio is not as easy in past the standard deviation of a is observed as 15.8% for stock a and 23.7% for Stock B if you think that the standard division of this portfolio is simply the weighted average of the two stocks that is 0.6 into 15.8% plus 0.4 into 23.7% equal to 19% this would be incorrect as a special case only if the prices of two stocks moved in a perfect lock step then only this computation would be true for any other case the diversification as we see shortly will reduce the risk below this figure for a simple two stock case the standard deviation of the portfolio is simply computed as shown in the figure here by filling all the boxes and adding them up the simple principle followed here is this the risk or variance of each stock is weighted by the square of the proportion invested in those stocks that is W1 square into Sigma 1 square + W2 square into Sigma 2 square and that portion of the risk that is on account of the co-variance between these stocks that is their common movement due to the effect of Market this covariance is expressed as the product of the correlation coefficient that is R12 and the two standard deviations that is covariance sigma12 equal to R12 into Sigma 1 into sigma2 if the two stocks move together then you would expect the correlation coefficient that is row one2 to be positive and therefore the covariance to be positive as well similarly if the two stocks move in a POS Direction then you would expect the correlation to be negative if the stocks are unrelated then we can expect the correlation coefficient and covariance to be closer to zero thus the resulting expression for our two stock portfolio can be computed as shown here portfolio variance equal to X1 s Sigma 1 s + X2 s Sigma 2 s + 2 * x1x2 Row 1 2 into Sigma 1 into Sigma 2 the portfolio standard deviation would be the square root of the portfolio variance let fill the above boxes with some numbers assume a correlation coefficient of one the portfolio risk box will look something like this as shown here in the table the resulting portfolio variance will be the sum of all these boxes that is portfolio variance equal to 0.6 ra to the^ 2 into 15.8 to the^ 2 + 2 into 0.6 into 0.4 into 1 into 15.8 into 23.7 + 0.4 ^ 2 into 23.7 ^ 2 equal to 359 .5 the standard deviation is square otk of 39.5 that is 19% this is exactly the same as the weighted average of these two variances this can be ascribed to the fact that we have considered a correlation of one let us now assume a correlation coefficient of Row 1 2 equal to 0.8 the resulting portfolio variance can be simply computed as shown here that is portfolio Vance equal to 0.6 ^ 2 into 15.8 ^ 2 + 2 * 0.6 into 0.4 into 0.18 into 15.8 into 23.7 plus 0.4 ^ 2 into 23.7 ^ 2 equal to 22.1 the standard deviation is square root of 22.1 that is equal to 14.6% the risk is reduced from that computed earlier in fact this is now less than both the stocks A and B considered individually this is a very interesting result it indicates that as the correlation or Co variance between the two stocks comes down the risk also comes down that means highest levels of diversification occurs if the correlation in the stocks is close to zero or negative consistently negative correlation over long periods is not observed at best fund managers try to select those stocks that have very low correlations over time let us consider a very hypothetical case of extreme negative correlation that is row1 to equal to minus1 in this case the portfolio variance is computed as shown here that is portfolio variance equal to 0.6 ^ 2 into 15.8 ^ 2 + 2 into 0.6 into 0.4 into -1 into 15.8 into 23.7 + 0.4 ^ 2 into 23.7 the^ 2 equal to Z in a theoretical world where a perfect negative correlation is available there is a set of security weights that result in zero variance risk however perfect negative correl ations do not exist in real markets the concepts developed here also hold for portfolio of multiple stocks let us develop the formula to compute the portfolio risks for a portfolio of multiple stocks we'll approach this problem in the same manner as filling boxes with respective risk components as earlier the diagonal boxes here represent the RIS weights associated with variances that is x² into Sigma Square the off diagonal boxes represent risk weights associated with covariance terms that is Xi XJ and into Sigma J let us consider a case of insecurities on a more practical note when we are adding Securities to a portfolio chances are that investments will not be extreme on either sides up or down that is one would invest amounts closer to average that is one upon n fraction of the proportion taking this assumption that is a more realistic assumption portfolio variance can be computed in the form of two components that is variance component and co-variance component thus there will be n variance terms let us represent the variance of these terms as an average variance measure then portfolio variance can be simply written as n into 1 upon n sare into average variance by so remember W1 into W2 into Sigma Square where W1 = to W2 = 1 upon n and sigma equal to average variance that is Sigma average the average variance is defined in a manner that if summed up across all the N boxes it will result in the variance or specific risk component of the portfolio that is n into 1 upon n² into average variance equal to n into 1 upon n² into Sigma average similarly we can Define the average covariance term that is Sigma covariance average here this average covariance reflects the market risk component that is the risk of the portfolio driven by the covariance across Securities if summed up across n Square - n columns that is n sare - n into 1 upon n sare into Sigma covariance average the overall combined portfolio variance term becomes portfolio variance equal to n into 1 upon n² into average variance plus n s - n into 1 upon n sare into average co-variance please note that as the number of Securities that is n in the portfolio increase the specific risk term that is n into one upon square into average variance approaches to a value of zero thus the overall portfolio variance approaches the average co-variance term this is also often referred to as portfolio diversification thus if these Securities have very low corelation then one can obtain a portfolio with a very low risk that is just by increasing the number of Securities in a portfolio one can eliminate the Ed syncretic or specific or diversifiable risk the remaining risk is often called Market risk or non- diversifiable risk that is why this Market risk or average covariance or non- diversifiable risk is what constitutes the Bedrock of risk that is risk which is thereafter eliminating all the specific risk to summarize in this video we discussed the computation of risk and return for a portfolio of stocks we started the discussion by showing how to compute the return and risk that is the standard deviation for a two- stock portfolio we noted that for a two stock portfolio the risk of the portfolio is lower than the weighted average of the risk of individual portfolio constituents we further observed that this reduction in the risk is determined by the correlation between these two portfolios for example if the correlation is negative and high in magnitude then the risk of the portfolio is considerably lower conversely if the correlation is positive and high in magnitude then the risk of the portfolio is considerably higher we extend our discussion of two stock portfolio to multi- stock portfolio and observed that as the number of stocks in a portfolio are increased the stock specific edos syncretic risk dies away in this multistock portfolio the only relevant RIS risk is Market risk impact of individual Securities on portfolio risk in this video we discuss the contribution of a security to the risk of the overall portfolio we also discussed the competation of beta a security sensitivity to Market movements lastly we also summarize the concept of value additivity individual Securities are volatile and risky investors usually add many Securities in their portfolio to diversify the stock specific osyn critic risk thus it is not the risk of a security held individually but in a portfolio that is important if the portfolio is well Diversified then only the market risk component of the stock that is non- diversifiable or systematic risk matters to the investors thus to measure the impact of a security to the risk of portfolio one needs to measure the market risk component of the security that is how sensitive a security is to Market movements the market risk of a security is measured through its beta that is the sensitivity of the stock to Market movements stocks with beta of more than one tend to amplify the movements of market stocks with beta between 0 to 1 tend to move in the same direction as Market but are considered less sensitivity the market portfolio has a bet of one and reflects the average movement of all the stocks in the market this is so because Market portfolio is often defined as the portfolio of all the stocks in a market consider a stock with beta of 1.4 over the given time Horizon this means that on average in that period when Market Rises by 1% stock a Will Rise by 1.41% if Market Falls by 2% then stock a is expected to fall by 2.82% on average if this stock does not have any stock specific ideosyncratic risk then its return profile can be easily plotted as shown here however the stock would also have some stock specific risk that means the actual returns would be scattered around this line and may not exactly fall on the straight line nonetheless when a stock is added to a well Diversified portfolio the movements on account of idiosyncratic factors are expected to cancel each other out therefore for this portfolio what matters is only these systematic Market related effects stocks like stock a here with high beta will have steep straight curve stocks with small beta for example beta equal to 0.3 the straight line plot will be less steep many times a stock with high beta also have high standard deviation but this is not always the case a stock with high beta may also have less edos syncretic risk and a stock with low beta may also have high idiosyncratic risk for example a stock with gold mining firm may have low beta and a very high idiosyncratic stock specific risk however when added to a well Diversified portfolio the edos syncretic risk of this gold firm may not matter what will matter is the market risk which is expected to be very low since the beta of this firm is expected to be very less so let us now answer this question how security betas affect the portfolio risk First Market risk accounts for most of the risk of a well Diversified portfolio bet of an individual security measures its sensitivity to Market movements thus it would be appropriate to summarize now that in the context of a portfolio beta would be a more appropriate measure of risk examine the figure shown here the standard deviation or the total risk of the portfolio depends on the number of Securities in the portfolio as the number of Securities increase in the portfolio more diversification is achieved the specific risk here declines until all the stock specific risk is eliminated and only Market risk remains that is why Market risk is often referred to as the Bedrock of risk as it remains steady Market risk depends on the average beat of the Securities that is the portfolio beta therefore if one selects a fairly large number of Securities from a market you diversify all the idiosyncratic risk and are left with the market risk only thus you get a portfolio which is very close to the market portfolio the beta of this portfolio is expected to be close to one for example if the market portfolio has a standard deviation of 20% Then This portfolio is expected to have a standard deviation of close to 20% consider the figure here here the green line shows a well Diversified portfolio with a beta of 1.0 if the market portfolio has a standard deviation of 20% Then This portfolio is also expected to have a standard deviation of 20% that is green curve for a well Diversified portfolio with a betat of 1.5 one can expect the standard deviation to be closer to 30% similarly if the portfolio beta is 0.5 then one can expect the portfolio standard deviation to be closer to 10% that is brown curve in summary the risk of a well Diversified portfolio is equal to the average betat of Securities in the portfolio beta of a stock I can be computed using the following formula that is beta equal to Sigma IM upon Sigma m² Sigma IM is the co-variance between the stock returns and market returns and sigma square m is the variance of the Returns on the market the ratio of this co-variance and variance is the contribution of the stock to the portfolio risk that is beta consider the example shown here in the table the returns from market and stock a are provided here returns from market and stock a are provided for 6 Monon period average returns for both these Investments are 2% variance of Market return is 50.67 and co-variance between the stock and Market is 76 beta for the stock works out to 1.5 they suggest that the stock a has particularly sensitive to Market movements column three computes the deviation in Market return and column four computes the square of these deviations column six provides deviation in stock a returns from their mean column 7 provides the deviation product that is column 3 into column 6 that is deviation in stock a and Market from their respective means multiplied with each other by now we have established that diversification reduces risk and makes sense for investors however can we say that a diversified firm is more attractive to investors than an undiversified firm if diversification is good objective for a firm to pursue then each new Project's contribution to form diversification should also add value to the firm the diversification package of f projects should be greater than the sum of the parts that also means that the present value of all these projects if added together would result in a higher value however this seems to be not consistent with what we have studied about present values this is true for the simple reason that investors can diversify for themselves in fact they can do so more easily than firms for example they can diversify in different industry sectors by directly buying these securities however for form to diversify in different industry sectors is extremely difficult for example to diversify in steel industry the investor only needs to pay security transaction charges and brokerage fee however for a firm to enter into a new domain such as steel would require huge amount of resources and time this leads us to the following conclusion if investors can diversify on their own they would not be paying anything extra to the firm for this diversification objective however there is an assumption of deep liquid and efficient financial markets that allow investors to choose Securities from different industry sector and riskiness as they wish that is why countries where large Capital markets are available that facilitate firms to diversify investors do not pay any additional price to firms that are Diversified in their project and businesses that is the total value of firm is equal to its parts this is the concept of value adity that is present value of any number of assets is equal to the present value of their parts that is present value of a b c taken together equal to present value of a plus present value of B plus present value of C separately this means that if a firm has three assets a b and c then the present values of a b and c cash flows taken together is same as the sum of their cash flow present values individually to summarize in this video we discussed the concept of beta that is sensitivity of a stock to Market movements we discussed that for a well Diversified portfolio the stock specific edos syncretic risk of a security is eliminated therefore only the market risk component of the security matters if the security is part of a well Diversified portfolio this Market risk component of a security is measured using its beta for example if the beta of a security is 1.5 then if the market moves by 1% the movement in Security on account of this market movement is 1.5% of course the security will also have some OS and cretic risk that not be that will not be related to this market movement however when the security is added to the portfolio comprising large number of Securities then these idiosyncratic movements will be eliminated through the process called diversification lastly we also discussed the concept of value additivity that is some of the different assets or project cash flows is same whether taken together or separately which means investors do not give any additional value to a firm if it obtains diversification with the help of adding more projects this is so because investors can diversify themselves by adding more Securities from different industry sectors in their portfolio assuming that deep and liquid financial markets are available to them to choose Securities from different industry sector and asset class groups if this is the case then the sum of different components that is Project assets cash flow present values is same whether considered separately or taken together as a unit that is present value of a BC equal to present value of a plus present value of B plus present value of C separately to summarize in this lesson we understand that returns to investor vary depending upon the risk bond by by them at one extreme very safe instruments such as treasury Securities provide the lowest returns as compared to this Equity Securities are considered to be more riskier asset class and offer higher expected returns this also indicates that while evaluating a safe project the discount rate to be applied to cash flows should be closer to the risk-free instrument such as try bill rates in contrast if you are valuing a risky project cash flows then the appropriate discounting rate should be closer to the more risky instruments like Equity Securities this also gives us two benchmarks for the opportunity cost of capital for evaluating project cash flows risk of a security means that there are many possible return outcomes for that security the more possibilities there are the higher the risk that security carries thus risk is a measure of spread of possible outcomes of a security price that is returns and is often measured as the standard deviation of a stock the risk or standard division of a stock has two components first stock specific risk and second Market risk risk is often evaluated more appropriately in the portfolio context investors eliminate a sizable portion of their risk simply by adding more Securities to their portfolio this diversification takes place due to the elimination of stock specific risk or idiosyncratic risk the second component that is Market risk cannot be eliminated through the diversification process a well Diversified portfolio is only exposed to Market risk that is unanticipated Market movements a securi contribution to a well Diversified portfolio measured as the sensitivity of the security to Market movements this sensitivity to Market movements is often measured as the beta of the security beta measures that percentage change in the stock price for 1 percentage change in the market value market is often measured or proxied through broad market indices such as S&P 500 or 50 betof Market is one which represents a portfolio carrying a large number of stocks in Market thus beta becomes the average of all the betas of the security in that market and hence is approximately one any security with beat of more than one is more sensitive to Market movements a stock with beat of less than one is less sensitive to Broad Market wise movements for a well Diversified portfolio the standard deviation is proportional to its beta that means for a well Diversified portfolio with beta equal to two we'll have a standard deviation that is twice of the standard deviation of a portfolio with beta equal to 1 while this diversification is a noble objective for an investor this does not mean that firm should also diversify by adding more projects simply to obtain diversification this is so because investors can obtain diversification on their own account if deep and liquid financial markets are available that means they will not pay any extra price for for a firm just because it is diversifying by adding more projects this also means that Pro value of a project assets present value of cash flows are same whether considered separately or taken together as a unit for a firm this is called the concept of value [Music] additivity [Music] [Music]