These risks result from external financial events and not from the nature of the issuing institution. RISK AND FLUCTUATION OF THE VALUE OF A SECURITY All of the above risks could adversely affect companies' financial performance and their future cash flows. Investors consider risk only to the extent that it affects the value of the security.
In a market economy, a security's risk is measured in terms of the volatility of its price (or of its rate of return). To begin with, it must be realized that a security's rate of return and the value of a financial security are actually two sides of the same coin. In an uncertain world, investors cannot calculate their return in advance, as the value of the security at the end of the period is unknown.
The standard deviation of individual assets is higher than the standard deviation of the entire market (as given by the market index). A better measure would be the covariance between the returns of the assets in the portfolio.
T HE FORMULA APPROACH
When an investor wants to know the contribution of risk to the portfolio rather than the total risk of an asset, what is the appropriate measure of risk that he should use. The standard deviation of a single asset is not the correct measure because the standard deviation measures risk in isolation without considering correlation with other assets. The correlation coefficient is a number between −1 (returns 100% inversely proportional to each other) and 1 (returns 100% proportional to each other).
Correlation coefficients are usually positive, since most stocks rise together in a bull market and fall together in a bear market. As the calculations above show, the overall risk of a portfolio consisting of Ericsson and Heineken shares is less than the weighted average of the risks of the two stocks. Although the swings in Ericsson and Heineken shares are positively correlated with each other, owning both together in a portfolio creates a less risky profile than investing in them individually.
Only a correlation coefficient of 1 creates a portfolio risk equal to the average of its component risks.
T HE MATRIX APPROACH
If we follow the diagonal cells from the upper left to the lower right, it should be noted that the number of conditions in the diagonal is always equal to the number of assets included in the portfolio. As a result, the “pool” of variances that can affect portfolio risk is equal to the number of assets included in the portfolio. There are many more covariances that increase rapidly as assets are added to the portfolio.
As with a two-asset portfolio, the variance of an N-asset portfolio is the sum of all cells of the matrix. Thus, the variance of the portfolio is most affected by the covariance because their higher number exceeds that of the variances. Then there will be N elements in the variance diagonal and N(N−1) – or N2−N – terms in the other cells.
This equation highlights the importance of the matrix method because, if we increase the number of assets included in the portfolio, the variance of the portfolio converges to the average covariance of the assets. However, it is now possible to understand the true meaning of what was previously defined as "market risk". This is the risk measured by covariance and represents the part of the risk that cannot be eliminated even after benefiting from diversification.
T HE BETA AS A MEASURE OF THE MARKET RISK OF A SINGLE SECURITY
The specific security risk J is equal to the standard deviation of the various residuals εJ from the regression line, expressed as σ(εJ), i.e.
C ALCULATING BETA
Given that Ericsson has a magnification effect of 1.36, his reasoning will be influenced by the fact that this stock will increase the risk of the portfolio.
P ARAMETERS BEHIND BETA
For illustration, the table below shows the betas, as of mid-2008, of the EuroSTOXX 50 stocks: The greater the effect of the state of the economy on a business sector, the higher its β value. Temporary work is such a very vulnerable sector. This serves to highlight how GM's financial health is, to some extent, a reflection of the health of the entire economy.
All other factors being equal, if a firm issues poor or low quality information, the β of its stock will be higher as the market will factor the lack of visibility into the stock price. CHOOSE BETWEEN MULTIPLE RISKY ASSETS AND THE EFFICIENT FRONTIER This section will address the following question: why is it correct to say that an asset's beta should be measured against the market portfolio. To begin with, it is useful to study the impact of the correlation coefficient on diversification.
If Ericsson and Heineken were perfectly correlated (i.e. the correlation coefficient is 1), diversification would have no effect. However, the chance of this happening is small because both companies are exposed to the same economic conditions. With a fixed correlation coefficient of 0.3, there are portfolios that offer different returns at the same risk level.
A portfolio consisting of two-thirds Heineken and one-third Ericsson thus exhibits the same risk (10%) as a portfolio consisting only of Heineken, but yields a return of 8.3% vs. As long as the correlation coefficient is below 1, diversification will be effective. download THE INFLUENCE OF THE CORRELATION COEFFICIENT ON RISK AND INTERRUPTION. Heineken is called the effective limit. download There is no reason for an investor to choose a given combination if someone else offers a better one. efficient) return at the same level of risk.
For every portfolio that is not on the efficient frontier, another can be found that, given the level of risk, offers a greater return or, for the same return, carries less risk.
R ISK - FREE ASSETS
Apart from all subjective elements, it is impossible to choose between portfolios that have different levels of risk. There is no universally optimal portfolio and therefore it is up to the investor to decide based on his risk appetite. He could even borrow money at a risk-free rate and use the funds to buy Heineken shares, but the risk on his portfolio would increase accordingly.
The expected return of this portfolio is equal to the risk-free rate, plus the difference between the expected return on Heineken and the risk-free rate. This difference is then weighted by the ratio of the standard deviation of the portfolio to the standard deviation of Heineken. For a portfolio that includes a risk-free asset, there is a linear relationship between expected return and risk.
To reduce portfolio risk, simply liquidate some portfolio stocks and put the proceeds into a risk-free asset. To increase the risk, all you have to do is borrow at a risk-free interest rate and invest in a risky stock.
R ISK - FREE ASSETS AND EFFICIENT FRONTIER
The line connecting the risk-free rate to portfolio M is tangent to the efficient frontier. Investors' taste for risk may vary, but the graph above shows that the wise investor should be invested in portfolio M. It is then a matter of adjusting the risk exposure by adding or subtracting risk-free assets.
The weighting of shares in a market portfolio will necessarily be the value of the individual security divided by the sum of all the assets.
C APITAL MARKET LINE
In a top-down approach, investors focus on the asset class (stocks, bonds, money market funds) and the international markets in which they wish to invest (ie the securities chosen are of minor importance). At the end of the spectrum, investors choose income stocks whose prices are relatively stable and provide the bulk of their return from dividends. Although the return on a portfolio of stocks is equal to the average return on the stocks in the portfolio, the risk of a portfolio is lower than the average risk of the stocks that make up the portfolio.
Those portfolios that are located on the part of the curve known as the efficient frontier will give better returns than those portfolios that are not. Including a risk-free asset in a portfolio leads to the creation of a new efficient frontier, which is the line connecting the risk-free asset to the market portfolio in the risk/return space. 21/What can you say about a stock for which the standard deviation of the return is high, and is low.
30/Show that the market portfolio must lie on the capital market line and on the part of the curve called the efficient frontier (see Section 21.2). 32/A the risk of a portfolio may be greater than the individual risk of each of the securities it contains. 33/In which circumstances the risk of a portfolio can be smaller than the individual risk of each of the securities it contains.
To help you, you have a record of the share price and the general index. What part of the total risk for the ENI share is explained by market risk. 1/The volatility of the asset's value is measured by the standard deviation of its return.
2/Relation between paper return and market return, paper market risk, regression line of paper return vs. 12/Because of the very poor visibility we currently have on what will happen in Internet stocks. 29/There should be no doubts about the solvency of the issuer, no risk to the rate at which the coupons can be reinvested and protection from inflation.
