| (1) Mixing many risky securities. | | | | (c) The consider mixing any one of these efficient |
| Portfolio theory has its roots in the management of | | | | portfolios, with a risk-free investment, Rf. |
| investors' portfolios of stock exchange investments | | | | Conclusion. |
| and fixed interest stocks. The following sections | | | | Out of all the possible portfolios that could be |
| show how the attempt to identify an optimal | | | | constructed from risky investment, only one portfolio |
| portfolio for investors has led to a comprehensive | | | | is worth considering-portfolio M. A combination of Rf |
| but simple theory of how the capital market relates | | | | and M produces portfolios which are better than any |
| risk and return. This, in turn, will assist us in our | | | | others in terms of the return which is offered for |
| attempt to adjust discount rates to allow for risk. | | | | any given level of risk. |
| The previous section considered portfolios of two | | | | However, given the existence of risk-free |
| securities. It is easy to expend this theory to cover | | | | investment, investors would choose form those on |
| portfolios of many securities, noting that where | | | | the revised efficient frontier represented by line RfM. |
| returns are assessed in percentage terms: | | | | Portfolios on the line RfM are achieved by mixing |
| (a) The expected return of a portfolio is equal to the | | | | portfolio M with risk-free investments. Portfolios on |
| weighted average of the returns of the individual | | | | the line M N are achieved by borrowing at the |
| securities in the portfolio. | | | | risk-free rate (remember we have assumed that the |
| (b) The risk of the portfolio depends on:i. The risk of | | | | risk-free rate applies to borrowing as well as lending) |
| each security in isolation:ii. The proportions in which | | | | and investing our own funds plus borrowed funds in |
| the securities are mixed:iii. The correlations between | | | | portfolio M. |
| every pair of securities in the portfolio. | | | | What is portfolio M. |
| (2). Efficient portfolios. | | | | Because we have assumed that all investors have |
| It is possible to identify which of these portfolios are | | | | the same expatiations about the future outcomes of |
| really worth holding. | | | | investments, it follows that: |
| A rational risk -adverse investor would define an | | | | All investors will come to the conclusion that portfolio |
| efficient portfolio as one that has.a). A higher return | | | | M is the best portfolio consisting solely of risky |
| than any other portfolio with the same risk; andb). A | | | | investments to hold. |
| lower risk than any other with the same return. | | | | Now, if any quoted share was not in portfolio M, |
| This simple approach is known as the mean-variance | | | | then nobody would with to hold it. It would therefore |
| efficiency rule (return = mean or expected return; | | | | have not value. We must therefore conclude that: |
| risk = variance or standard deviation). | | | | Portfolio M includes every risky security which is |
| So, out of all the possible portfolios which an investor | | | | quoted on the market. |
| could make out of his chosen securities, which are | | | | Portfolio M is in fact simply a slice of the whole stock |
| mean variance efficient? (Put another way, which | | | | market; the proportions of shares held in it are the |
| portfolios would the investor select from, given logical | | | | same as the total market capitalization of the shares |
| assessment of the mean returns and variances of all | | | | on the stock market: |
| those available). | | | | Portfolio M is called the market portfolio. |
| You need to be familiar with the following | | | | All rational risk- averse investors will hold the market |
| terminology. | | | | portfolio, according to the model we have jest |
| (a). Domination an investment dominates another if it | | | | constructed. Note that it is not necessary for very |
| provides a better return for the same risk or less risk | | | | investor to hold very share on the stock market. |
| for the same return. | | | | Replicas of portfolio M may be generated by holding |
| (b). An efficient investment is one which is not | | | | as few as fifteen shares. Investment in unit trusts |
| dominated by any other investment, where as an | | | | will also achieve the same result. |
| inefficient investment is one which is dominated. | | | | However, all investors do not have the same attitude |
| (c). Investor utility curves (or indifference curves) are | | | | to risk. By using the market portfolio, and by either |
| curves alone which the investor is indifferent | | | | lending or borrowing suitably at the risk-free rate, the |
| between the combinations of risk and return. | | | | investor can choose any level of risk he likes and can |
| (d). Optimal portfolio- the efficient portfolio that has | | | | predict the return which the market will give him. This |
| the highest utility for a given investor. This idea was | | | | return will be the best that he could possibly get for |
| discussed at the start of the chapter & | | | | the risk taken. |
| identifying this portfolio requires knowledge of the | | | | (4) Constructing the capital market line. |
| investor's indifference curves. | | | | We have already seen that combinations of risk-free |
| (3). The market portfolio. | | | | and investments give a straight line trade-off |
| The assumptions | | | | between risk and return. |
| A few assumptions are now made, in order to build a | | | | To draw the capital market line we therefore need |
| simple model: | | | | only two observations, |
| (a) Investors base their portfolio investment decisions | | | | 1. Rf- The risk-free rate of interest, which can be |
| on expected returns, standard deviation and | | | | approximated by the return on government stock. |
| correlations between all pairs of investments. | | | | 2. Rm and sigma m- The risk and return of the |
| (b) All investor have the same expectations about | | | | market portfolio. As the market portfolio should |
| future outcomes over a one-period time horizon. | | | | contain all risk investments, this can be estimated by |
| (c) Investors may lend and borrow without limit at | | | | using the risk and return on a stock market index |
| the risk-free rate of interest. | | | | such as the Financial times all share index. |
| (d) There are no market imperfections: investments | | | | Value of the Capital market line. |
| are infinitely divisible, information is costless, there are | | | | The capital market line tells us for a given level 0 risk |
| no taxes, transaction costs or interest rate charges, | | | | the return an investor should expect on the stock |
| and no inflation. | | | | exchange. It is often referred to as giving the |
| Some of these assumptions are obviously unrealistic, | | | | market price of risk. That is if we choose to take a |
| but they greatly simplify the model- building process. | | | | given level of risk on the stock exchange then we |
| Furthermore, even if the assumptions are relaxed, | | | | can expect a given level of return. If this is less than |
| the theory will still hold approximately. | | | | that offered by the project, it is tempting to say |
| Building the model. | | | | that the project should be accepted. However, there |
| (a) Firstly , consider all the portfolio which could be | | | | is a flaw in this logic. |
| constructed out of risky securities quoted on the | | | | The problem with this analysis is not in determining |
| stock market. | | | | the capital market line but in determining the risk of |
| (b) Then identify the efficient portfolios from these. | | | | an individual investment. |