Learning Material Sample

Investment principles, markets and environment

2. Portfolio Risks and Returns

In this section, we describe various types of risk that could affect investments. Our audiovisual presentation helps illustrate the types of risk.

Risk to capital

This is the risk that some/all of the individual capital invested may be lost. The possibility of this risk usually increases where investments provide the potential for higher real returns.

“Unsystematic risk” is the risk of some internal or external event that can affect the performance of one company (and therefore value/earnings etc for the investor), but may not necessarily affect other institutions. A common...

Shortened demo course. See details at foot of page.

...rent view of that country’s prospects with the effects this may have on relevant assets held.

Liquidity risk

An investment may be difficult to sell e.g. unlisted company shares.

Settlement or counterparty risk

The counterparty to a transaction may fail to settle.

No investment will be free of any risk due to the fact that some risk will be associated with capital loss, and some with the nature or level of returns that can be gained. We will see later on in this chapter how the risks of a portfolio can be managed to a minimum, in order to provide the maximum returns.


In this section we discuss the concepts behind calculating annualised returns accounting for both capital growth and income streams received during the term being measured.


The basic concept behind portfolio theory is to strike a balance between the level of risk that attaches to a portfolio in relation to the desired level of returns.

Some of the more straightforward measurements of return on certain investments e.g. dividend yields of equities etc, will not take into account all capital inflows / outflows. In addition they don’t provide a calculation that can be used for all investments in order to compare “like with like”.

Holding Period Return

To compare “like with like” it is necessary to provide a calculation which accounts for all income received during the investment period plus any capital gain made. It does not however, take account of any taxation applying to the investor or the timing of receipts of income and capital.

The calculation formula is:

       (D + Ps – Pa)

R =  ---------------- x 100%



R = the holding period return

D = the returns received in the period

Pa = the price at acquisition

Ps = the price on selling (actual or anticipated)

In addition to make a valid comparison between each investment, the returns should be annualised. This will account for the fact that the calculation of returns using the above formula may be derived from different time periods...

Shortened demo course. See details at foot of page.

... we see that the returns of 15% and 30% are the most frequent and there is therefore a 6 in 20 chance of achieving the same result this year. This is expressed as a probability of 0.3.

Average returns

When calculating average returns, we need again to be sure that we are comparing “like with like”. There are three main descriptions of “average”.

The “mode” is the most popular return from a given set of figures. In our previous example, the mode average is 15% or 30% as they each occur on 6 out of the 20 occasions.

The “median” return is the return where half of the time the investment performed better and half of the time it performed worse. In this case, the median return is somewhere between 15% and 30%.

The “mean” average return can be classified as an “expected rate of return”. From our example on the previous page we firstly calculate the weighted probability of each return and total the results to find out the mean average return. This is shown below:


One-year return

R (%)



Weighted probability

R x P
















This calculation is the same as adding up all returns (total of 490 in our example) and then dividing by the total number of occasions in this case 20. As you will imagine, using a large portfolio of several assets and several periods of returns, calculating mean averages using the weighted probability method above can be considerably quicker.


In this section we discuss the measurement of risk with a portfolio of investments.


In order to assess the attractiveness of expected (probable) returns, we also need to assess the level of risk that is being taken.

To some a certain level of risk may not be acceptable. It also goes without saying that if the same expected returns can be achieved from a product that is lower risk when compared to another, investors would normally opt for the lower risk product (all other factors being equal).


Investments GHI and JKL have the following possible returns and probabilities of those returns:

Investment GHI

One year return

R (%)



Weighted probability

R x P (%)











Expected return


Investment JKL

One year return

R (%)



Weighted probability

R x P (%)











Expected return


Both GHI and JKL investment have the same expected returns. However, JKL is riskier as in year 1 it produced a negative ret...

Shortened demo course. See details at foot of page.

...the square root of these variance figures

Using Investment JKL from the previous example, we can manually calculate standard deviation as follows:


Difference from the mean (15.5)

Difference Squared

Difference squared multiplied by the probability

















The standard deviation will be the square root of 299.296875 = 17.30 (rounded down)

The smaller the standard deviation of the performance return of an asset is, the more predictable and less volatile it is.

As a rough guide, 68% of returns are distributed within one standard deviation on each side of the mean average (expected) return.

Approximately 95% of returns are distributed within two standard deviations of the mean and nearly all returns are within 3 standard deviations of the mean.

Where returns are not close to the mean i.e. they have a higher standard deviation, they are considered more risky.

We will go onto to see another measurement of risk that applies to the relationship between an investment and the market as a whole (beta), but next we consider ways to reduce risk using certain methods.



In this section we discuss two key methods used to reduce risk within investment portfolios.


An investment portfolio manager can reduce risk within his portfolio of securities by using investments such as derivatives like futures and options to take a counter position to the direction in which he feels that his portfolio ...

Shortened demo course. See details at foot of page.

... it demonstrates a point. This is likely to produce the most effective diversification if it can be achieved.

No Correlation

Returns from some companies are not related in any way to others. For example an English firm making furniture for the domestic market will not be correlated with a South African gold mining firm.


In this section we discuss the use of modern portfolio theory within risk reduction working alongside maximising returns within a portfolio.


Modern portfolio theory builds on the concepts of diversification and provides a mathematical justification for them. This theoretical work confirmed that if returns on assets are not perfectly correctly, then the greater the diversification of a portfolio, the lower the level of risk associated with any given return. It is the combined effects of a portfolio’s assets, that are important not the risks and returns of the individual component parts.

The efficient frontier

Modern Portfolio theory can be used to cre...

Shortened demo course. See details at foot of page.

...urity and the relationship that they have with each other in terms of the variance of their returns (correlation). This is measured by the covariance of returns.

Covariance of returns

Where two securities are affected by the same market factors and influences, they will be defined as having a positive covariance. If one moves in a positive direction in a given set of circumstances whilst the other moves the opposite way in the same circumstances, the two securities will be said to have a negative covariance. This association will vary between -1 (complete negative covariance) and +1 (complete positive covariance).

The mathematical calculation for this association is:


In this section we discuss the limits to which risk can be diversified.

As we have seen from our calculations on the previous pages, the more securities that ...

Shortened demo course. See details at foot of page.

... covariance of returns.

The concept of risk reduction through diversification is illustrated below:

Risk of portfolio (standard deviation of returns)


In this final section we discuss the management of systematic risk.

The Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) was a development of Modern Portfolio Theory introduced in the 1960s. It provides a model to estimate whether the expected returns from a portfolio are sufficient given the amount of risk being taken. It is a linear model linking risk and returns. Effectively CAPM states that the total risk of a security is a combination of systematic and non-systematic risk. Non-systematic risk (as already seen) can be eliminated through diversification of the portfolio. The investor therefore faces only systematic risk, the extent to which a security is correlated to the market as a whole. CAPM identifies a measure of this risk known as “beta”. It establishes a linear relationship between beta and re...

Shortened demo course. See details at foot of page.

...ay be considered a simplistic approach.

Arbitrage Pricing theory (APT) offers an alternative to CAPM in that it works on the principle that the expected risk premium of a security depends upon a number of factors and the security’s exposure to them.

Such factors can be market or industry related, macroeconomic variables, etc. Some securities will be more sensitive to certain variables than others. The expected risk premium on each security will depend upon the expected risk premium associated with each factor and the particular security’s sensitivity to each of these factors.

According to APT, the equilibrium expected return of a security is the risk free rate plus the sum of a series of risk premiums, multiplied by the security’s beta factor, while CAPM assumes prices to be determined solely by market risk.


About Demo Courses

This is a shortened version of our online course, built so that you can get a good idea of what is provided. The full version shows all the current text and is fully formatted. Use the top right drop down menu to view the chapters. If you have already purchased this course, please log in to access the full version

Our online courses page lists details of all our courses. For more details on the above course see;

Chapter Links