# Essay Sample - Investment theory

*1. Discuss how the investor can use the separation theorem and utility theory to produce an efficient portfolio suitable for the investor's level of risk tolerance?*

*2. Futures contracts use daily mark to market to calculate the amounts in margin accounts. Explain how mark to market accounting reduces risk to investors in futures markets?*

*3. Discuss the major assumptions that are made in formulating the Capital Asset Pricing Model. How realistic are these assumptions in valuing a real world security? *

1. Discuss how the investor can use the separation theorem and utility theory to produce an efficient portfolio suitable for the investor's level of risk tolerance?

The method used in selecting the optimal portfolio uses “indifference curves”. They reflect the attitude of investors to risk and return and can be represented as a graph on the horizontal axis of which are the risk values, the measure of which is the standard deviation, and on the vertical axis - the value of the remuneration, the measure of which is expected return. The first important property of indifference curves is that all the portfolios presented at a given indifference curve, are equivalent to the investor. The second important feature of indifference curves is: the investor will consider any portfolio presented in the indifference curve that is above and to the left, more attractive than any portfolio presented on the indifference curve, which is below and to the right. Investors, forming portfolio, are seeking to maximize the expected return on their investments at a certain acceptable for them level of risk (and vice-versa, to minimize the risk at the expected level of profitability). The portfolio that meets these requirements is called efficient portfolio. The most preferable for investor efficient portfolio is optimal.

The investor chooses his optimal portfolio of a variety of portfolios, each of which provides: the maximum expected return for a certain level of risk; minimal risk for some value of expected return. A set of portfolios that satisfies these two conditions, is called the effective set. Moreover, of particular importance are the portfolios that are on the border of this set.

The pricing model of capital assets (CAPM) is based on the fact that investors, who invest in risky assets, expect some extra income in excess of the risk-free rate of return as compensation for the risk of owning the assets. Such a requirement is described by the technical term “risk aversion”. Investors, not taking the risk, not obligatory avoid it. However, they require compensation in the form of an additional expected return for taking the risk on investments, the yield of which is not guaranteed.

CAPM assumes that the rate of return on risky asset is made up of the rate of return on risk-free assets (risk-free rate) and the risk premium, which is associated with the level of risk on the asset. Due to the fact that all investors have the same effective set, the only reason why they choose different portfolios is that they are characterized by indifference curves.

Although the selected portfolios are different, each investor will choose the same combination of risky securities. This means that each investor will allocate his funds among riskier securities in the same relative proportion, increasing the risk-free borrowing or lending in order to achieve a preferred for him combination for risk and return. This property of capital asset pricing model is often called the separation theorem: “The optimum for the investor combination of assets does not depend on his preferences for risk and return”. In other words, the optimal combination of risky assets may be determined without constructing indifference curves of each investor.

The explanation for the separation theorem is that all portfolios positioned on a linear effective set, include investing in “tangential” portfolio, combined with different levels of risk-free borrowing or lending.

2. Futures contracts use daily mark to market to calculate the amounts in margin accounts. Explain how mark to market accounting reduces risk to investors in futures markets?

The clearing house every day carries out daily mark to market of the futures contracts in accordance with the current market prices. If the contract is a loss, then requirements to depositing of additional security is exposed to ensure that the margin is not less than the amount requested (minimum margin). If on the investor's margin account the amount is accumulated that is greater than the lower margin level, he can use this surplus, debiting it from the account.

For each type of contract the exchange sets a limit deviation of futures prices of the day on the quoted price of the previous day. If the futures price moves beyond the specified limit, the Exchange halts trading contracts, which plays an important role in reducing the risk of large losses and in prevent bankruptcies. This situation continues as long until the futures price will be included in the limit range. In order to limit speculative activity Exchange also establishes certain position limits, i.e., limits the number of contracts that can be kept open by one investor, and a breakdown of the time of their calculation.

3. Discuss the major assumptions that are made in formulating the Capital Asset Pricing Model. How realistic are these assumptions in valuing a real world security?

Capital Asset Pricing Model (CAPM) serves as the theoretical basis for a number of different financial technologies of management of the risk and yield applicable to the long-term and medium-term investments in shares. The model is constructed based on a number of assumptions.

1. Investors evaluate portfolios by comparing the expected return and the variance (standard deviation) of each portfolio in a single holding period, indicating the normal distribution of random variables of yield of portfolio securities.

2. The investors act rationally and, given the choice between two identical portfolios (with the same level of risk), always choose the portfolio that offers higher returns.

3. All investors seek to avoid unnecessary risk, i.e. of two identical portfolios with the same yields, they always choose the portfolio with lower risk.

4. Each of funds can be divided into an unlimited number of parts, and the investor is able to buy any desired proportion of the security.

5. There is a risk-free securities, deprived of any risk - inserting money into these funds do not bear any risk and provides investors with the risk-free rate of return rf. Rf rate is the same for all investors.

6. There are no obstacles for investors to commit acts of buying and selling financial assets, taxes and fees are not taken into account, it is believed that investors do not bear the costs of diversification.

7. There is no uncertainty about the expected rate of inflation, that is, prices of all financial assets include the inflationary component and fully reflect changes in inflation expectations.

8. All the information on the functioning of financial markets is absolutely available for any investor.

According to the model, there are two types of risk associated with investment in any risky financial instruments: systematic risk and non-systematic one. Still, CAPM model is rather theoretical model and can be used in practice only in general way. However, it allows to get a benchmark rate of return, which can be used to assess prospective investments. Second, this model allows to make grounded assumptions about the expected return on assets that have not yet traded in the market. Despite the fact that the CAPM does not withstand the test of practice, this fact does not prevent its widespread dissemination, which is explained by in-depth understanding of the essence of the described processes, which the model provides.