Economics and the Equity Market: A Microeconomics Course Application

Economics encompasses two broad subjects: macroeconomics and microeconomics. Macroeconomics deals with an economy in aggregate and addresses issues such as inflation, unemployment, interest rates, and economic growth. We present a macroeconomic perspective in Chap. 10.1007/978-3-030-74817-3_3. Microeconomics, the focus of this chapter, operates, as its name indicates, on the micro level, addressing household consumption decisions and the production decisions of firms. In this chapter, we focus on the parallels (and a few differences) between a standard microeconomics formulation (a household’s selection of an optimal consumption bundle) and a standard finance model (an investor’s selection of a portfolio that optimally combines a riskless asset – cash – and a risky equity portfolio). The finance formulation is the Capital Asset Pricing Model (CAPM). CAPM is a keystone of what is known as modern portfolio theory, the originator of which is Harry Markowitz who was awarded a Nobel Memorial Prize in Economic Sciences in 1990 for having developed the theory of portfolio choice. We then introduce friction (trading costs) and show how CAPM’s frictionless market equilibrium is perturbed. The analysis provides a good lead-in to the next chapter on finance.

The impact of long-term riskless asset on ensuring liquidity and preventing banking fragility

PurposeThrough portfolio diversification, the author identifies the risk sharing deposit contract in a three-period model that maximizes the ex ante expected utility of depositors.Design/methodology/approachIn this paper, the author extends the study by Allen and Gale (1998) by adding a long-term riskless investment opportunity to the original portfolio of a short-term liquid asset and a long-term risky illiquid asset.FindingsUnlike Allen and Gale, there are no information-based bank runs in equilibrium. In addition, the model can improve consumers' welfare over the Allen and Gale model. The author also shows that the bank will choose to liquidate the cheaper investments, in terms of the gain-loss ratios for the two types of existing long-term assets, when there is liquidity shortage in some cases. Such a policy reduces the liquidation cost and enables the bank to meet the outstanding liability to depositors without large liquidation losses.Originality/valueThe author believe that the reader would be interested in this article because it is relevant to real world where depositors rush to withdraw their deposits from a bank if there is negative information about future prospect of the bank asset portfolio and bank investment. Economists and financial analysts need to determine the suitable mechanism to improve the stability of the bank and the depositor welfare.

A New Set of Financial Instruments

In complete markets there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for hedging derivatives assuming that a hedger should not always rely on trading existing assets that are used to form a linear portfolio comprised of the risky asset, the riskless asset, and standard derivatives, but rather should design a set of specific, most-suited financial instruments for the hedging problem. We introduce a sequence of new financial instruments best suited for hedging jump-diffusion and stochastic volatility market models. The new instruments we introduce are perpetual derivatives. More specifically, they are options with perpetual maturities. In a financial market where perpetual derivatives are introduced, there is a new set of partial and partial-integro differential equations for pricing derivatives. Our analysis demonstrates that the set of new financial instruments together with a risk measure called the tail-loss ratio measure defined by the new instrument’s return series can be potentially used as an early warning system for a market crash.

MINIMIZING THE PROBABILITY OF LIFETIME RUIN: TWO RISKLESS ASSETS WITH TRANSACTION COSTS

We compute the optimal investment strategy for an individual who wishes to minimize her probability of lifetime ruin. The financial market in which she invests consists of two riskless assets. One riskless asset is a money market, and she consumes from that account. The other riskless asset is a bond that earns a higher interest rate than the money market, but buying and selling bonds are subject to proportional transaction costs. We consider the following three cases. (1) The individual is allowed to borrow from both riskless assets; ruin occurs if total imputed wealth reaches zero. Under the optimal strategy, the individual does not sell short the bond. However, she might wish to borrow from the money market to fund her consumption. Thus, in the next two cases, we seek to limit borrowing from that account. (2) We assume that the individual pays a higher rate to borrow than she earns on the money market. (3) The individual is not allowed to borrow from either asset; ruin occurs if both the money market and bond accounts reach zero wealth. We prove that the borrowing rate in case (2) acts as a parameter connecting the two seemingly unrelated cases (1) and (3).

Who would invest only in the risk-free asset?

Within the setup of continuous-time semimartingale financial markets, we show that a multiprior Gilboa–Schmeidler minimax expected utility maximizer forms a portfolio consisting only of the riskless asset if and only if among the investor’s priors there exists a probability measure under which all admissible wealth processes are supermartingales. Furthermore, we show that under a certain attainability condition (which is always valid in finite or complete markets) this is also equivalent to the existence of an equivalent (local) martingale measure among the investor’s priors. As an example, we generalize a no betting result due to Dow and Werlang.

Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics II: Economic Implications

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs; we allow cash dividends on the risky asset. The allocation shifts toward the riskless asset relative to diffusion in varying degrees depending on parameter values. It is sensitive to the proportion of the jump component to total volatility, but also to the expected amplitude for a given proportion. The shift becomes small when the relative risk aversion increases, but it becomes major when the solvency constraint is active in the presence of jumps. We derive utility losses and risk premia due to jumps under realistic parameter values, and show that even when the no transaction region is very similar between pure diffusion and the mixed process the latter corresponds to lower utility because of higher portfolio restructuring costs.

The Eminence Of Risk-Free Rates In Portfolio Management: A South African Perspective

The traditional Capital Asset Pricing Model (CAPM) suggests that the minimum return required by an investor should be equal to the return of a risk-free asset (Reilly & Brown, 2003), which should be stable (Reilly & Brown, 2006), not influenced by external factors (Harrington, 1987), and certain (Bodie, Kane & Marcus, 2010). Evidence, however, suggests that risk-free asset returns vary (Brunnermeier, 2008), and that “there is really no such thing as a truly riskless asset” (Brigham & Ehrhardt, 2005:312). The pioneering studies of Mehra and Prescott (1985) and Weil (1989) only justified the size of the equity premium and risk-free rate puzzle but failed to provide a consensus on the specifications for the most ideal risk-free rate proxies. The results from this paper accentuated the problem of selecting a risk-free rate proxy, as all proxies under evaluation exhibited a level of risk and volatile returns. No regularities between the pre-, during and post-financial crisis regarding the choice of most ideal risk-free rate proxy were found. Overall findings suggested that the ideal proxies are the 3-month T-Bill rate and the 3-month NCD rate for the pre-, during and post-financial crisis periods, respectively.

On the role of Föllmer-Schweizer minimal martingale measure in risk-sensitive control asset management

Kuroda and Nagai (2002) stated that the factor process in risk-sensitive control asset management is stable under the Föllmer-Schweizer minimal martingale measure. Fleming and Sheu (2002) and, more recently, Föllmer and Schweizer (2010) observed that the role of the minimal martingale measure in this portfolio optimization is yet to be established. In this paper we aim to address this question by explicitly connecting the optimal wealth allocation to the minimal martingale measure. We achieve this by using a ‘trick’ of observing this problem in the context of model uncertainty via a two person zero sum stochastic differential game between the investor and an antagonistic market that provides a probability measure. We obtain some startling insights. Firstly, if short selling is not permitted and the factor process evolves under the minimal martingale measure, then the investor's optimal strategy can only be to invest in the riskless asset (i.e. the no-regret strategy). Secondly, if the factor process and the stock price process have independent noise, then, even if the market allows short-selling, the optimal strategy for the investor must be the no-regret strategy while the factor process will evolve under the minimal martingale measure.