Indifference Curve Analysis
The Inventory-Theoretic Approach to Money Demand
and the Demand for Cash Balances
The portfolio model is based on the notion that individuals hold portfolios containing both cash and securities or other financial assets. The goal of these individuals is to maximize the expected return 'E[R]' of a particular portfolio while trying at the same time to minimize the financial risk 'r' associated with that portfolio. This optimization problem can be stated as follows:
max U = f(E[Return], risk)What is unique about the objective function is that it contains an economic good (Return) and an economic bad (risk) or:
dU/dR > 0 and dU/dr <0
Expected return in this model is the total dollar return from the portfolio (interest, coupon or dividend payments) and risk is based on the variability of these returns in a given portfolio. Risky portfolios may pay higher returns but there is an equal probability of large losses. Less risky portfolios involve lower returns but also smaller losses. Utility-maximizing investors seek to maximize return and minimize the risk associated with any portfolio subject to the risk-return combinations defined by financial markets.
Indifference curves represent the wealth-holder's preferences for expected return on a portfolio (a good) and the risk associated with that portfolio (a bad).
One method to minimize risk is for an investor to hold all of his/her wealth in cash. Given this approach there is a zero probability of a loss (with the exception of inflation risk). However, holding all cash also means a zero rate of return. Holding the entire portfolio in securities may maximize the return but perhaps at an unacceptable level of risk. These indifference curves represents individual preferences that will allow for the determination of an optimal combination of cash and securities given an investor's preferences for risk and return (some individuals might be risk-seeking, other individuals are risk-averse).Measures of risk.
Risk is often measured by taking a historical look at the variability of the return in an asset over time. This variability may be computed using a variance or some other measure of variation:
Where the larger the variance for a particular asset the greater the risk. As an extension, when making a comparison among different assets this variance measure must be scaled to adjust for the magnitude of the dollar-value of the returns being considered. This scaling is accomplished simply by dividing the measure of variation by the mean of the returns:
The optimum is found where a given indifference curve is just tangent to a market-determined risk-return locus.. This locus represents actual combinations of risk and return as determined by primary and secondary financial markets.The Risk-Return Locus
In the diagram below, risk is measured in the horizontal axis and expected return 'E[Return]' is measured on the vertical axis. The indifference curves I0, I1, I2, are upward sloping representing the fact that return is desired by the investor and risk is normally avoided by the investor. The point where an indifference curve intersects the vertical axis represents the level of risk for "risk-free" assets such as government securities.
Any point of tangency between an indifference curve and the risk-return represents an optimum -- a point where the preferences of the investor match exactly with the reality of the market.
Concepts for Review: