Applied Fundamentals in Finance

The risk–return characteristics of individual assets play an important role in both portfolio construction and performance evaluation. In this chapter, the main focus is on returns. First, the periodic investment return is presented, which can be calculated as a simple (discrete) and continuous compounded return and for one or more periods. This is followed by an examination of the average returns of investments, which can be determined using the arithmetic or the geometric mean. While the performance of an investment can be assessed on the basis of the geometric mean return, the performance evaluation of an investor is carried out using the money-weighted return. In addition, the asset return can be broken down into a nominal and real component. The expected return consists of the risk-free interest rate and a risk premium and can be estimated using, for example, historical returns or a prospective scenario analysis.

As with returns, there are different measures of risk, and it is difficult to find a general consensus on how to define risk. The perception of risk varies among market participants and depends, among other things, on the composition of the portfolio, the type of investor (private or institutional), and the investor’s attitude to risk. For a pension fund or insurance company, for example, the risk is that liabilities are not covered by assets. The risk of a mutual fund is characterised by the deviation of the portfolio’s return from a benchmark. A private investor, on the other hand, defines risk as the possibility of their investment decreasing in value as the result of a loss. In this chapter, various risk measures are presented. The variance or standard deviation as well as downside risk measures, such as the semi-standard deviation and the value at risk, are discussed.

The assumption that returns are normally distributed is very convenient, as only the first two moments of the distribution (i.e. the mean and the variance) are required to fully describe the return distribution. However, in the vast majority of cases, financial asset returns are not normally distributed, and higher central moments of the distribution such as skewness and kurtosis must therefore be considered. In addition, the market characteristics of investments are also important for their evaluation. The price of financial assets is affected by the information efficiency and liquidity of the markets. The latter has a significant impact on the level of trading costs. If the assumptions of normal distribution do not apply, and if market information efficiency and market liquidity are not given, higher central moments of the distribution such as skewness and kurtosis, as well as market characteristics, must be considered in order to be able to assess the investment. In addition to the higher central moments of a distribution such as skewness and kurtosis, the longnormal distribution is also presented in this chapter. Afterwards, the market properties of investments such as the information efficiency of financial markets, random movement, and market liquidity and its influence on trading costs are described.

Rather than investing in a single asset, most investors put their money into a portfolio of assets. This raises the question of how to calculate the expected return and risk of a portfolio. Furthermore, it has to be determined which portfolios of risky assets are most efficient in terms of expected return and risk. Markowitz’s portfolio theory demonstrates how to construct the efficient frontier on which the most efficient risky portfolios lie with regard to expected return and risk. The efficient frontier is created from capital market data, which are used to estimate the expected return and standard deviation of the returns of individual assets, as well as the covariance or correlation coefficient between the returns of a pair of assets. This chapter describes how to calculate the expected return and risk of a portfolio of risky assets. It then demonstrates how the efficient frontier can be determined using historical return data. The chapter ends with a discussion of the diversification effect and the number of stocks required for a well-diversified portfolio.

In addition to the return–risk characteristics of the assets, the investor’s attitude to risk must also be taken into account in order to achieve the investment objectives. This chapter demonstrates how the efficient frontier is combined with the investor-specific indifference curves to arrive at the optimal risky portfolio. The efficient frontier is constructed using capital market data with the expected return and standard deviation of returns on individual assets and the covariance or correlation coefficient between returns of pairs of assets. Indifference curves, by contrast, measure the benefit the investor gains from holding the portfolio. In calculating the benefit or utility, relevant factors include the degree of risk aversion of an individual investor, in addition to the expected return and the risk. The point of contact between the efficient frontier and the highest possible investor-specific indifference curve represents the optimal portfolio of risky assets. If the risk-free asset is included in the portfolio construction, the optimal portfolio lies on the most efficient capital allocation line. Assuming that market participants have identical (homogeneous) capital market expectations, then all investors invest in the same portfolio of risky assets or market portfolio. All investment combinations of the risk-free asset and the market portfolio lie on the capital market line.

Investors want to be compensated for taking higher risk by a higher expected return. This raises the question of the level of return compensation. In financial market theory, this question is answered by one-factor and multifactor models which determine the expected return of a single asset or a portfolio of assets with one or more systematic risk factors. The most widely used model is probably the capital asset pricing model (CAPM). With this one-factor model, which is typically applied to equity securities, the expected return of a stock or stock portfolio is calculated by adding a risk premium to the risk-free rate. The former is the product of the expected equity market risk premium and the beta of the investment. The higher (lower) the systematic risk or market risk of the investment, the higher (lower) the beta and hence the expected return. However, empirical studies on equity securities demonstrate that stock returns are correlated not only with equity market returns but also with other factors. Two of these risk factors are the size of the firm (measured by market capitalisation) and the book-to-price ratio, which were captured by Eugène Fama and Kenneth French in a multifactor model. The Fama–French model (FFM) is a three-factor model that explains expected returns in terms of risk premiums and the corresponding betas for market, size, and value. Both the CAPM and the FFM are based on the assumption that investors are compensated by a premium when they assume systematic risk. Hence, only systematic risk is relevant to valuation. These two models differ in how systematic risk is measured. In the CAPM, the systematic risk is given by the market portfolio, whereas the FFM uses size and value as systematic risk factors in addition to the market portfolio. This chapter examines these two models.

The portfolio management process consists of various steps and ensures the systematic construction of a portfolio that is appropriate to the client’s needs. The process consists of three phases, namely planning, execution, and feedback. In the planning phase, the financial markets and investor needs are analysed, the long-term investment policy is formulated, and the strategic asset allocation is determined. In the execution phase, the portfolio is created and the assets required by the investment policy are purchased. The feedback phase concludes the process and includes monitoring of the investment policy and capital market expectations, as well as rebalancing and performance evaluation of the portfolio.

Equity analysis is carried out by means of fundamental and/or technical analysis. Fundamental analysis examines the factors influencing the share price that are relevant to valuation. For this purpose, information on the overall economy, the industry, and the company are analysed. Central to fundamental analysis is a valuation model on the basis of which the intrinsic value is calculated. To arrive at an investment decision, the intrinsic value determined with the valuation model is compared with the market price. If the intrinsic value exceeds (falls below) the market price, the equity security appears to be undervalued (overvalued). The valuation models applied in fundamental analysis can be divided into absolute and relative models. The absolute models can be grouped into cash flow models and value-added models. Cash flow models include the dividend discount model, the free cash flow to equity model, and the free cash flow to firm model. This chapter presents the dividend discount model, which, like the other cash flow models, is used to calculate the intrinsic share value under the going concern assumption. According to the model, the intrinsic value equals the present value of the future dividends that investors can expect when buying stocks. For this purpose, future dividends are discounted with the expected return of the shareholders.

Cash flow models include not only the dividend discount model but also free cash flow models, in which free cash flows are discounted at the expected rate of return instead of dividends. Free cash flows are the operating cash flows generated by the company less the net capital expenditures that are required for its operating activities. They can be determined either after payment of the debt provider claims (free cash flows to equity) or before these claims are paid (free cash flows to firm). The advantage of these valuation models is that they are conceptually sound and suitable for most equity valuation applications. The free cash flow to equity model and the free cash flow to firm model are presented in this chapter. The adjusted present value model, which is a further development of the free cash flow to firm model, is also described.

The intrinsic value of an equity security is determined on the basis of a cash flow model using the growth rate of the cash flows and the expected return. Relative valuation analysis, on the other hand, assesses the value of an equity security against a benchmark employing a multiple. This approach makes it possible to examine whether the security is valued correctly relative to the stocks of comparable companies. The fundamental economic principle of the comparables method is based on the law of one price, according to which two identical assets are traded at the same price. A distinction is made between price multiples and value multiples. With a price multiple, the price of an equity security is set in relation to a financial variable that has a significant influence on the share price. The variable chosen for this purpose is, for example, the earnings or the book value per share. The intuition behind value multiples is similar. Investors evaluate the market value of an entire company relative to the amount of earnings before interest, taxes, depreciation and amortisation (EBITDA), sales, operating cash flow, or free cash flow to firm. Thus, the enterprise value is considered in relation to a financial variable that affects its value. This chapter examines the price-to-earnings ratio, the price/earnings-to-growth ratio, and the price-to-book ratio as examples of price multiples. It goes on to discuss the enterprise value EBITDA ratio, which belongs to the value multiples.

Bonds belong to the traditional asset classes together with equity securities. These are interest-bearing securities that are securitised and thus tradable. The global bond market is large and diverse and offers important investment opportunities, especially for institutional investors. Its importance can also be seen in the fact that bond markets are larger than equity markets worldwide. In contrast to equity securities, the majority of fixed-income securities are traded over the counter. An understanding of bonds is useful as these securities increase the universe of investments available to create a diversified portfolio. The chapter first deals with the basics and the various types of bonds, followed by the pricing of option-free bonds with the cash flow model. In addition to the pricing of fixed-rate bonds, the pricing of floating-rate bonds is also examined. The chapter concludes with a discussion of the three yield measures of current yield, yield to maturity, and total return, which allow investors to assess the return on their investment in fixed-rate option-free bonds.

The relationship between the bond price and the expected return is negative. If the expected return increases (decreases), the price of the bond decreases (increases). The changes in the yield to maturity result from a change in the benchmark rate and the risk premium. The latter is a return compensation for credit risk of the issuer and market liquidity risk of the bond. The risk of a bond is analysed using the sensitivity measures of modified duration and modified convexity. These risk measures can be used to assess how much the bond price changes when the expected return (or the yield to maturity) moves. Duration improves with convexity in view of the fact that the relationship between price and yield to maturity of a fixed-rate bond is not linear. This chapter starts with an analysis of the risk factors relevant for bond valuation. This is followed by a presentation of the duration-convexity approach, which can be derived from the second-order Taylor series expansion. Next, Macaulay duration, modified duration, and modified convexity are described. Finally, the chapter examines applications of duration and convexity in portfolio management, which can be used for tactical asset allocation, investment strategies, such as the immunisation strategy, and for exploiting and hedging predicted interest rate and credit risk changes.

Derivatives can be divided into forward commitments and contingent claims. A forward commitment. is a contractual agreement between two parties, which involves an obligation to buy or sell an underlying asset at the expiration date of the contract and at a price that is specified at the start of the agreement. Examples are futures and forwards, which differ in that the former are traded on an exchange and the latter over the counter. Swaps also belong to the category of forward commitments and, like forwards, are traded over the counter. By contrast, a contingent claim grants the buyer the right to buy (call option) or to sell (put option) the underlying asset at the agreed strike price either during or at the end of the option life. The option seller, on the other hand, has the obligation to sell (call option) or buy (put option) the underlying asset at the strike price. The chapter begins with the use of derivatives, which includes risk hedging, risk-taking (speculation and trading), and the exploitation of price differences (arbitrage). After differentiating between futures and forwards, the calculation of profit/loss, price, and value is explained. This is followed by a discussion of how forwards and futures can be applied to hedge risky positions. The chapter ends with an examination of interest rate swaps.

Options, like futures and forwards, are derivative instruments that provide the opportunity to buy or sell an underlying asset with a specific expiration date. However, a long option gives the holder the right, not the obligation, to buy (call) or sell (put) an underlying asset. On the other hand, the holder of the short option or the option seller has the obligation to fulfil the option buyer’s right to buy or sell. For the right to purchase or sell an underlying asset, an option premium is paid from the buyer to the seller of the option. By contrast, futures and forwards involve no cash upfront payment. The chapter begins with the basic characteristics and the profit and loss calculation of call and put options. This is followed by an examination of option pricing using the one-stage and two-stage binomial model, the Black–Scholes model, and put–call parity. The leverage is then described, which reflects the return leverage of options against the underlying asset. The chapter ends with the option price sensitivities. They allow to examine how much the option price changes when a risk factor (e.g. price or price volatility of underlying) moves. Options on individual stocks, also called equity options, are among the most popular and are subsequently used to illustrate the profit and loss calculation, the pricing, the leverage effect, and the option price sensitivities.

Calls and puts can be used in a variety of ways. They allow market participants to modify a risk position or implement an investment strategy. Some option strategies have been designed to make a profit if a certain market condition occurs and are therefore purely speculative in nature. Other strategies, however, are defensive and allow protection against an unfavourable market development. This chapter describes the use of options in typical investment situations. The chapter begins with put–call parity, which can be applied to create synthetic long–short positions of an equity security, a call option, and a put option. It goes on to explain how the risk exposure of a long equity position can be modified with a covered call and a protective put strategy and in which situations the respective strategy is appropriate. Another option strategy associated with hedging the price risk exposure of a long equity security is a collar, where a price floor and a price ceiling are set on the underlying asset. If the share price falls outside these price limits, there is no further loss or gain. The chapter ends with option strategies that can be constructed from a combination of calls and puts with different strike prices—strategies such as bull and bear spreads, as well as the straddle.