Portfolio Statistics

Portfolio Statistics

To begin by reviewing the most basic concepts of macroeconomics, inflation is calculated as a percentage change from one year to the next. To calculate the percentage change between two values, one subtracts the new value from the old value, divides the result by the old value and then multiplies by a 100. Real values are corrected for inflation while nominal values are not.

Someone who is risk averse seeks to minimize risk, whereas someone who is risk neutral wants to maximize return, even if that means taking some risk. Theoretically, there may also be a risk-loving category, but the notion seems more appropriate to gambling than to financial management. The difference lays primarily in prioritization.

The rationale behind diversification: to attain the efficient portfolio frontier (the goal), one must maximize expected return [r], and minimize variance [Ø]. The r = n over square root of Ø; therefore, assuming all assets [n] are independent, by increasing the amount of assets (diversifying) one may reduce the variance to nearly 0. Closely related are the maximin (maximizing minimum gain) and minimax (minimizing maximum loss) statistical concepts.

A tangency portfolio is the result of a computation, the combination of stocks and bonds that should be held according to the equation to calculate the expected rate of return. A leveraged portfolio means capital was borrowed to create the portfolio. One of the most crucial models in finance is the capital asset pricing model (CAPM). Developed by Markowitz (1959), Sharpe (1964) and Lintner (1965), the CAPM assumes that all investors are rational and consequently choose to hold a tangency portfolio (which is sometimes far from the truth).  Tangency portfolio must thus equal the actual market portfolio.

But we had a pretty diversified portfolio of businesses around the world and things tended to offset each other. But one or two years ago, we had a lot of things happening at the same time (Jim Cantalupo). Photo: Megan Jorgensen (Elena)

The term ‘equity premium puzzle’ was coined by economists Prescott and Mehra (1985). An equity premium is the difference between the return on stocks and on bonds over a period of time; over intervals of long duration, stocks appear to outperform bonds. Logically, it follows that if someone wants to invest in the long tem (more than 30 years), then there seems to be little incentive to invest in the consistently underperforming short debt, but is anything ever so simple? Because most individuals are risk averse, they prefer to invest in governmental bonds, which are virtually riskless.

However, these theories are often misused. Experienced, successful investors may believe that they do not need diversification. Also, theories look great on paper, but in practice may be difficult to implement or even inefficient. According to the media, many governments are overinvested in oil, which would not be the case if the theory were applied.

References:

• Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47(1): 13-37.
• Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1): 77-99.
• Mehra, R. & Prescott, E.C. (1985). The equity premium: A puzzle. Journal of Monetary Economics, 15(2): 145-61.
• Sharpe, W.F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3): 425-42.