Finance

Introduction
Portfolio theory and Capital asset pricing model are financial tools which helps the investors and analyst. It helps analyst and investors to decide the type of shares they would like to have in their portfolio and the expected return from that stock. Though it is based on historical data still it helps analyst and investor to decide the future action.

This tool also helps the investor identify the risk he is taking on his investments. Since, every investor has a risk appetite so he can decide the stock he would like to have in his portfolio. He can calculate the amount of return he will get for a specific level of risk so it act as a measure by which he can identify the growth he will get on his investments.

Portfolio Theory
Introduction
This theory helps analyst to decide the shares they would like to offer a potential investor for a specific level of risk. Since, diversifying helps to reduce risk this act as a great tool as it helps to reduce the risk for a specific level of return. This helps to make the investment more secure and get a higher return.

2.2 Description
Portfolio theory is an important financial tool which helps investors and researchers. According to Titman (2003) it specifies that, the risk for an investor can be minimised by creating a portfolio for an expected level of return. Every investor wants a good return on their stock for a specific level of risk. Portfolio theory helps to create those desired portfolios. This theory according to Ross Randolph, Bradford  Roberts (2007) says, As return increases risk also increases but after a certain point the return doesnt increases in the same proportion as risk. Suppose for example a person holds a single share of a company. Then the risk involved is high as the price may move up or down in relation to the market but in case we have a bundle of securities then a downward movement in one share is compensated by an upward movement in the other. This helps to reduce the risk.

This theory by Titman (2003) says that as it is used by analyst and managers to see how much return a portfolio gives and the amount of risk they have to bear for it. Then they try to compare the result and if there are deviations they work on improving the portfolio of securities. This is done so that the analyst can understand the risk taking ability of the investor
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2.3 Calculation of portfolio risk
This theory is important because it helps investors to diversify the risk undertaken by them. For example suppose an investor invest 65 of his money in Infosys and 35 in Intel.  The return on Infosys is 10 and Intel is 20. The expected return on his portfolio is
Infosys is 10 x 65  6.5
Intel it is 20 x 35  7.0.
The expected return on your portfolio is 6.5  7.0  13.50.
Now lets assume that a correlation coefficient of 1
Standard Deviation of Infosys  31.5 (i.e. the risk associated)
 Standard Deviation of Intel  58.5 (i.e. the risk associated)
So, the portfolio risk is  (.65) X (.65) X (31.5) X (31.5)  (.35) X (.35) X (58.5) X (58.5) 2(.65 X .35 X 31.5 X 58.5)  1006.1

There for the portfolio risk is sq root of 1006.1 which is 31.7. So, we see that the return of the investor increases at the same time the risk decreases. Thus investors prefer this model as it helps to quantify his risk for a return.

2.4 Efficient frontier of portfolio
The other reason supported by Ross Randolph, Bradford  Roberts (2007) as to why this theory is so relevant is that, combining stocks help to reduce risk. This is shown in the efficient frontier which measures all the combination of securities and the risk and return associated with them. It is shown in the following figure.

Here, the investor would want to be in the 3rd box as the return is highest and the risk involved is lowest. In the case of 4th box the return is higher but the risk is much higher compared to the return. Investors always want to move towards box 3. This helps an investor identify where he lies and how his stock is performing in relation to the market and what all needs to be done to make his investment safe.

2.5 Advantages
This also helps the investor know how their stock is moving in relation to the market. It has been pointed out by Keith  Dirk (2008) that, Combination of fixed income securities like bond and equities will help the investor know how their stock is moving with the market. This would make investor desire for such a portfolio where one stock moves in one direction and the other in another.

The reason pointed out by Nolan (2009), is that it compares the market risk associated with each asset in the portfolio. Since, it considers every single aspect so the recommendations that come on the basis of it are sounder.

A more thorough understanding of the market reveals that markets tend to grow in the long run. This has been supported by Essential Portfolio Theory (2009) by showing that, a longer horizon typically takes a fish hook shape which resembles the efficient frontier. Thus, if an investor has the correct portfolio of stocks then he can benefit in the long run as the risk reduces over a longer horizon.
This is seen as a common phenomenon that investors dont worry about the future as analyst provides a forecast for it. Since, forecast is done on historical data after taking into consideration all that is happening in the market and economy still there is a high risk of choosing the wrong stock.

This theory also helps investors to identify the return they would receive if they have a risk free security and a risky security while comparing it with two risky securities. It will thus according to Peng (2000) help them, decide whether he should invest in risky securities or risk free securities as it helps to identify his ability to take risk.

Bob (2008) pointed out that, portfolio theory helps conservative investors to gain more compared to aggressive investors. This is so because a conservative investor has the advantage of moving up higher on the efficient frontier line as compared to an aggressive one.

2.6 Drawbacks
In spite of this theory being so relevant still concerns has been raised regarding it. Bob (2008) in his study found that, investors believe that that their portfolios are diversified in individual stocks, mutual funds, bonds, and international stocks. While these are all different investments, still they are all in the same asset class and generally move in concert with each other. This makes their investment risky as seen in the recent market crashes.

Since, it is done by human there is a bit of subjectivity involved which might lead to the creation of portfolio not being correct as there could be biasness.

Capital Asset Pricing Model

3.1 Introduction
This model has been of great help to the financial sector. It helps to identify the return a stock gives for a level of risk. It helps to gauge the extra return that would be available to the investors up and above the risk free rate. This helps the analyst to decide on the stocks they would like to offer to an investor depending on his ability to take risk.

Investors are also greatly benefited from this model. Since, they can calculate the additional return they would receive over the risk free security so they can decide whether they would like to invest in a particular security or not.

3.2 Description
The capital asset pricing model gives a better picture for the investors. Ross, Randolph, Bradford  Roberts  (2007) pointed out that, Capital asset pricing model is used to determine the required rate of return of an asset, if that asset is added to an already well-diversified portfolio, given the assets non-diversifiable risk.

It is useful for investors because it helps them to calculate the price for a security or portfolio on the whole. It helps the investor to find out the extra return they will get compared to what they would have received had they invested in fixed income securities. Thus it is calculated as
Expected return of an asset  risk free return  beta expected excess rate of return  risk free return
This helps an investor to identify how risky his investment is. According to Antony (2008), it helps an investor to identify how the securities behave in relation to the market. It is illustrated in the following diagram how it holds relevance for the investor

It shows the investor that above the risk free rate he earns extra premium because of the risk involved. This helps him identify the fact that his investment has given him proper return. This will also help the investor to decide whether he wants to invest in a particular security as he can see the risk he has to bear while investing in a particular investment.

Now, according to Ross Randolph, Bradford  Roberts (2007), when we try to see both this models together it presents a clearer picture for the investor as he knows where his security lies in the efficient frontier. This is explained below

Here we see that the investor realizes where is security is. He would want his security to touch the frontier as that would be optimizing his return. This would make the investor know which assets suits his portfolio as it will determine the return he is getting at that level of risk.

3.3 Calculation of return on an asset
Lets look at an example to see its calculation
Return on government securities is 8
The beta (risk factor) is 1.8
Market Return for B Ltd is 10.5
Then the expected return is  8  1.8 (10.5 - 8)
                                             12.5
This helps the investors decide whether he would invest in that particular security. He would do so only if the actual return is more than the expected return. This would help him identify whether his stock lies in the efficient frontier line and decide whether he should invest or not in that security.

3.4 Advantages
Thus, according to George (2007), it is an important tool for equity researchers and analyst as it helps in project appraisal. It can be used to compare projects of different risk classes and is therefore superior to a net present value approach which uses only one discount rate for all projects, regardless of their risk.

Glenn (2002) also points that, this model is of great help to investor as it helps him to theoretically calculate the price of a stock or investment. The investor can calculate the value and find out whether the stock is over rated or under rated. This will help him decide whether he needs to invest in that particular investment or not. It will thus help him find out whether the market reflects the correct value and will also help him gauge the efficiency of the market.

As pointed out by Singh (2008) it help analyst to determine the cost of equity for the firm and estimate the required return for business. It also helps to determine the hurdle rates for corporate investments and to evaluate the performance of investment division in terms of costs and returns.

3.5 Drawbacks
In spite of it being used worldwide Willkie (1997) has pointed out that, Capital Asset Pricing Model doesnt work for different investor in different currencies. Here this theory assumes that investors have measured their risk in the same currency, but when currency changes, as in case of imports and exports than this model doesnt give the correct value and the expected return varies. This is so more because countries vary in size so its difficult to arrive at equilibrium.

Since, it uses the historical method for calculating the return so it might not give the actual return as the actual conditions prevalent in the market might be different from what the historical data reflects.

Conclusion
These two models are of great help to the investors and also the equity researchers. This helps them to take vital decision regarding the investment in a particular security. It helps them decide whether they would invest in a security for a prescribed level of risk.

Both these tools have helped to identify the stocks and have been in use for a long time. This has increased the efficiency of both this model. This is helping both the investor and the analyst as it is an easy model for calculation and does not involve the complexities which are prevalent in other models.