The equity markets are mostly controlled by the actions of fund managers and subsequently the investors that they advice. These are largely risk based markets where while there is possibility of great profit, there is also the possibility of tremendous loss. Fund managers and investors take the help of many different tools to ensure good returns on their investments. Using the portfolio theory they can figure out what kind of risk they will be subjected to against projected returns. The capital asset pricing model is basically a step forward from the portfolio theory and further evaluates the risks that an investor will be bearing upon buying a portfolio; under the assumption that this is risk that the investor will have to bear no matter what he does. Fund managers and investors need to decide whether an investment is worth making based upon this information. Although the two help bring to light the various aspects of market risk, they are still not 100% reliable, which will be further discussed.

The portfolio theory revolves around the selection of the best investment strategies in terms of risk, which focuses on the risk surrounding the equity market and the return or gains from any transactions. In essence an investor or fund manager would need to look at the portfolio theory to make a clear contrast between what is risk and what is simply uncertainty. The fact is that any discussion of an equity market will need some insight on the aspects of the risk associated with any venture or portfolio. This is imperative due to the nature of the equity business that is primarily based on risk itself, and also has a hand in defining the way market values of investments are given foundation (Brentani, 2004).

Eiteman (2008) classifies the core of a portfolio theory when he writes,

"The risk of a portfolio is measured by the ratio of the variance of the portfolio's return relative to the variance of the market return" (p 645)

It is the idea of risk versus return which is mainly what attracts an investor or fund manager to a portfolio. Theoretically speaking, one would want to create such a portfolio which offered an insight into the best risk-return opportunities against the given set of risk constrictions. This would enable the investor to increase the chances of maximizing his returns. An efficient portfolio will not only help him do this but also attain a higher return as opposed to a lower one.

Practically speaking, using the portfolio theory is important because the outcome of risk and return is unknown. It is because of risk that there is more than one possibility for an investor or fund manager; this includes returns that are on the mark, higher or even lower than previously expected. Without doing the proper research and looking into a proper portfolio, investing would be like throwing perfectly good funds down a well. However, the simple fact remains that just by having an idea of the risk does not mean that you can necessarily avoid it.

In terms of the portfolio theory, think of the risk of a single security; the risk will be taken in terms of the typical divergence on its returns. An example would be two assets, X and Y. suppose Asset X gives you a return over a period of four years during which it turns up 8.5%, 11.5%, 8%, and 12% respectively. Take the average one year holding on Asset X to be over 10%. While if you look at Asset Y you can see that for the same period of holding it gives a return of 8%, where as it has a return of 9%, 7%, 6.5%, and 9.5% respectively. For both the assets the divergence is 2% and 1.5% correspondingly. Based upon the past performance of both, we can assume that Asset X will continue to give out a higher return. This analysis makes the decision on what to invest in easier. That being said the divergence is higher for Asset X and that must also be taken into consideration. This is a very basic example of the relationship between risk and return which indicates that one should only bear with a higher risk if there is an expectation that there will be a greater return.

Now, the situation gets a little more complicated when the value of two deviations comes into the play. Two assets can be thrown together in a portfolio to form a sort of correlation, i.e. instead of pitting asset X and Y against each other we consider them jointly. We can use the previous example to make sense out of this. Asset X and Y are projected to have a 10% and 8% return respectively. In the first year X shows a 1.5% smaller return, where as Y shows a 1% higher return than expected. In the second year X gives a higher return by 1.5%, while Y shows a decrease by 1%. In the third year X gives out a 2% decrease in the expected return and Y is also 1.5% lower than the projected return. The last year shows that X gives a 2% higher return while B gives a 1.5% higher return than the one projected.

So when we look at X and Y, the average would be = (-1.5 x 1), (1.5 x -1), (-2 x-1.5), and (2 x 1.5). Our result will come out at 0.0001, which through a process of equivalence we can convert to 0.33. Now, we can see that a +1 correlation shows that the two assets work well together and vice versa. This helps us figure out the diversification of the two. We can after this further examine the portfolio and see how much of each, X and Y, the investors or fund managers want to add to their portfolio. For example they may want to have 80% of X and only 20% of Y based on the information that they have. The best payoff would be when the correlation between the two would be -1 because then this would indicate that there are some set of portfolio weights which eliminate risk.

Diversification is a handy tool because if you combine a higher returning asset to a lower risk asset than you increase your expected return. You have not only made your portfolio more efficient because of the higher expected return but have also inadvertently made your investments a safer one. This is successfully achieved with assets whose correlation is relatively lower as compared to others (Lumby, 1988).

After diversification we come to multiple asset portfolios. An effective portfolio gives investors the highest amount of return on any given risk; to achieve this they can invest in a variety of different stocks at the same time. The size of the company that is selling its stocks and shares is not important; it is the return that the investors or fund managers should be keeping an eye at. It would also be beneficial to diversify across markets, both international and domestically and get a hold of different kinds of assets e.g. stocks, bonds, properties etc, instead of sticking to one single method. If you have a well formed portfolio the basic idea is that there will be no haphazard risk attached to your investment. If not constructed properly, an ill managed portfolio can result in a great loss for the investing party. It is also important to remember that most of the risk can be diversified and taken care of but that does not mean that risk diminishes completely (Freeman, 2001).

Stemming from the portfolio theory is another model that addresses the matters of equity. The Capital Asset Pricing Model (CAPM) delves into measuring the risk of an asset and to take that risk and then define the given price as per the required return. The basic idea behind the CAPM is that there is some amount of risk that is associated with all assets in a capital market and this risk is not one that any investor can evade, this does not take into account the risk that the investor effectively avoids due to diversification. Ergo what we look at through this model is the effect that leftover risk after diversification will have on the investment. This gives the investors and fund manager a clearer idea of what to expect. We assume that all investors will have to bear this risk and all investors only care about risk and return. It gives them a fair idea of the risk involved in the portfolio they are interested in buying (Wormald et al., 2007).

The main idea is that investors want to trade off both risk and return. Here we assume that the demand and supply of capital assets is equal, while the prices remain at equilibrium. The rate of lending is also taken to be the same as the rate of borrowing, whereby the risk, if any, if small because all loans are assumed to be returnable. This is done to form some kind of solidity in the assumptions because otherwise the entire model would fluctuate and the results would be haphazard.

We set up the risks and returns of several portfolio possibilities to see the general effect. There will be a combination where no other assets will give out a better return at the same risk or a lower risk at the same return. This point would make the given portfolio a mean-variance efficient. The assumption is that is all borrowing and lending was suspended all investors would cling to the mean-variance efficient portfolios only, based on their own risk tolerance. In the event that this restriction is lifted then investors can achieve better profits, even better than the mean-variance efficient point (Bierman & Smidt, 1975). Therefore being able to borrow and lend create the possibility to divide an investor's preference of risk and return from the prospects that exist in the capital market. In essence the result would be that each investor would acquire the same portfolio of risk based assets, however, the market portfolio and rise-free assets would be different for all.

There are some complications that come with the CAPM; to begin with the model cannot be put to an actual test because you can never define any portfolio will a complete and total precision for example you can never define the components of the portfolio to an accurate degree (Armitage, 2005) i.e. can commodities be includes, is real estate addable to the model? Can antiques be made part of the overall picture? There are some assets that do not surface onto the markets very often and hence no real pattern of returns can be constructed for them. There are also those assets that do no have a set value, or those whose value will fluctuate over a matter of time, but they are an important part of the overall portfolio mix. An example would be the labor income; it cannot be traded and yet is an integral part of the overall assumptions.

No one particular set portfolio exists for all investors, each investor has to create one according to their preferences and in terms of the assets they are interested in acquiring. For those without a lot of funds this can prove to be a problem because the entire process requires a lot of hard work and lengthy research, which not all of them can afford. Some information that is available to one investor might not be given out to all investors. Also it is assumed that all investors have the same expectations on returns, which is not true (Gallati, 2003). Some risk maybe small for an investor and very high for another, so a singular method cannot be applied and a uniform portfolio cannot serve everyone's purpose.

The investors or fund managers will then have to choose something that gives them the most security and makes sense to their investment plans.

Armitage, S. (2005): *The cost of capital: intermediate theory*: Cambridge University Press

Bierman Jr., H., & Smidt, S. (1975). *Application of the Capital Asset Pricing Model to Multi-period Investments. Journal of Business Finance & Accounting*, 2(3), 327-340.

Brentani, C. (2004): *Portfolio management in practice: Essential capital markets corporate finance essentials*: Butterworth-Heinemann

Eiteman. (2008): *Multinational Business Finance, 10/e*: Pearson Education India

Freeman, L. (2001). *Diversification may increase returns and lower risks*. Ophthalmology Times, 26(12), 12.

Gallati, R. (2003): *Risk management and capital adequacy:* McGraw-Hill Professional

Lumby, S. (1988): *Investment appraisal and financing decisions:* Taylor & Francis

Wormald, M., Flynn, D., Uliana, E., Correia, C. (2007): *Financial Management:* Juta and Company Limited

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