 # Modern portfolio theory Figure 15: two-asset portfolio: near perfect positive correlation: COR = -F0.98 Figure 16: two-asset portfolio: near perfect negative correlation: COR = -0.97

Modern portfolio theory (MPT) was presented by Prof Harry Markowitz in a paper of 1952 and it remains relevant. In a nutshell it postulates that each share has an expected return and risk (measured by standard deviation), and by investing in a number of shares the investor can garner the benefit of diversification, and the benefit is a reduction in the riskiness (standard deviation) of the portfolio. MPT measures the benefit of diversification in the form of a lower standard deviation for the portfolio than the average for the shares that make up the portfolio. The benefit of diversification rests on the relatedness of the returns of the shares (i.e. the correlations).

Figures 15 and 16 demonstrate the principle. We have a two-asset portfolio made up of Share P and Share Q. In Figure 15 their returns are positively correlated (correlation coefficient - COR = +0.98). The average return is 25% pa and the standard deviation (STD) of the portfolio is 12.2%. In Figure 16 the shares' returns are negatively correlated (COR = -0.97). Note that the average return remains at 25% pa, but the STD is now 2.0%. This is because the volatility of the average return around the mean return (25% pa) is lower.

According to the MPT it is possible to construct an efficient frontier of optimal portfolios that offer the maximum possible expected return for a given level of risk, or the least risk for a given level of return. The benefit of diversification is intuitive and is known in general parlance as "not putting all your eggs into one basket". This is a significant principle in investments.

# Capital asset pricing model

The capital asset pricing model (CAPM) is an extension of MPT. It is a model that describes the relationship between risk and expected return (positive as we have seen) and is used in the pricing of risky securities. It says that investors in risky assets need to be compensated by two components (the total of which is called the required rate of return - rrr): the time value of money in the form of the risk-free rate (rfr) and a premium for risk (rp). The latter is calculated by a risk measure [beta, which is a measure of how the share has performed relative to the return in the market (rm) of which it is a part] times the rp: As we have said (and will further elucidate later), the CAPM formula is used in the valuation of shares (i.e. risky assets).

# Behavioural finance theory

Behavioural finance theory (BFT) proposes psychology-based influences to explain share market incongruity [divergence between fair value prices (FVP) and market prices]. Conventional theories such as EMH and CAPM assume that investors behave rationally, and emotions and other exogenous influences do not influence investors. In other words, the conventional theories can explain rational behavior in the financial markets, but the real world proves to be one in which participants often behave irrationally and unpredictably.

BFT fills the gap, and it assumes that, in addition to market information, the personal characteristics of participants (investors, speculators and arbitrageurs) influence their investment decisions and therefore market outcomes - which cannot be explained by the EMH and CAPM. A manifestation of BFT is the expression "herd behavior".

# Fundamental analysis (aka firm foundation theory) (security valuation)

## Introduction

Fundamental analysis (aka the firm foundation theory45) was mentioned earlier, and it postulates that investment assets have an intrinsic value (i.e. a fair value price - FVP) which is founded on the time value of money (TVM) concept (i.e. interest rates, which is encapsulated in the PV-FV concept). Figure 17: market price (MP) versus fair value price (FVP)

Figure 17 portrays the real world in respect of the asset markets: the market prices of assets (and this applies especially to shares) much of the time are not equal to their FVP, but are related to this underpinning factor, and generally reflect FVP on average over time. As we saw there are a number of theories that describe this phenomenon of deviation from FVP, including the castle-in-the-air theory and behavioural finance theory (BFT).

As said, the principle underlying asset valuation is the familiar FV-PV concept. A reminder is presented in Figure 17. The asset has a cash flow in the future (FV) and is discounted to PV, which is the value of the security now. The figure indicates just one interest payment in the future. When more are involved, compounding enters the picture, and the formula changes slightly to [cp = compounding periods pa (annually = 1, semi-annually = 2); y = number of years]:  Figure 18: time value of money (FV to PV) In this section we cover:

- Valuation of shares.

- Valuation of fixed-interest securities.

- Valuation of futures and options.

- Valuation of income-producing property.

- Valuation of commodities.

- Valuation of other real assets.

- Valuation of participation interests.