Mandelbrot and Volatility Clustering: The Intuition behind GARCH

Large changes tend to be followed by large changes, small changes by small changes, observed Mandelbrot (1963). In other words, you get persistence in the amplitudes of price changes.

Such observations in financial time series have paved the way for models like ARCH (Engle, 1982) and GARCH (Bollerslev, 1986). These aim to describe volatility clustering and kurtosis. GARCH was one of the first models to take into account volatility clustering.

Rama Cont has written a paper on volatility clustering where he proposes an agent-based explanation for clustering based on investor inertia.

The Milton Friedman Effect on the Currency Futures Market

Milton Friedman was an American economist born in New York and economic advisor to Ronald Reagan. He has done a lot of work on monetary policy and stabilisation (including rethinking the Phillip's Curve) and co-invention of currency futures, introduced by the CME in 1972. Friedman was paid $7,500 for a feasibility study on "The Need for a Futures Market in Currencies."

Prospect Theory and "Psychological Finance"

Theory that describes decisions between alternatives that involve risk, i.e. decisions between uncertain outcomes where probabilities are known. The model is DESCRIPTIVE i.e. attempts to model real-life choices, rather than optimal decisions.

It was developed by Kahneman(Princeton) and Tversky in 1979 as a pyschologically realistic alternative to expected utility theory. The theory describes how individuals evaluate losses and gains.

Immunizing Bond Porfolios

Fabozzi Chapter 19 talks about immunization of bond portfolios, i.e. hedging out the interest rate risk and the reinvestment risk. Matching durations for bonds of different maturities exposes you to reinvestment risk (the risk that you cannot invest the coupons at the IRR). A passive strategy is one that does not require rebalancing.

The Intuition Behind Bond Immunization

The concept of "immunising" a portfolio to changes in interest rates is core to bond portfolio management and asset-liability management in banks.

Immunization, also known as multiperiod immunization, can be described in different ways in different books.

One purported goal of immunization is to minimise the reinvestment risk (the ability to reinvest coupons at the IRR). Reinvestment risk is one of the major risks of the bond (together with interest rate risk, slightly different idea, basically if you are long the bond, you face the risk of rates rising sharply).

Fabozzi Chapter 19 talks about classical immunization is creating a bond portfolio to have a fixed return for a specific time horizon, no matter what happens to interest rates (i.e. you're hedging out the interest rate risk and reinvestment risk).

Duration matching means finding a bond of same duration as your portfolio to zero out the interest rate risk. If you have a 5 year liability and hedge with a 4 year liability you are exposed to reinvestment risk.

Active strategies are those that require rebalancing. Why so? Because the duration of the portfolio keeps changing with rates. It is not a linear function of time. The portfolio and the hedge (if we divide it into two parts) get out of step in terms of duration - the durations no longer match. How often should you rebalance is an open question.

"Classical" techniques of immunization assume parallel shifts in the yield curve. Vasicek and Fong (Journal of Finance article, 1984) established a measure for immunization risk versus arbitrary rate changes.

minimising immunization risk == minimizing reinvestment risk

Princeton University's CEPS Series

Princeton University has a series of working papers called CEPS, referring to the "Center for Economic Policy Studies". Amongst these are papers by Burton Malkiel on "Bubbles in Asset Prices" (January 2010) and "The EMH and its Critics" (April 2003).

The World Price of Foreign Exchange Risk

Bernard Dumas is a Professor at INSEAD specialising in International Finance. Together with Bruno Solnik, a professor at HEC Paris, he published a paper in 1995 in the Journal of Finance (one of the most widely-cited academic journals in finance). It tackles the problem of making asset-pricing models ("APM"s) international. Basically the concept is if you own international assets (which will be defined later), the risk premia in your calculations must factor in the fact the covariances of assets with exchange rates as well as the covariance with the market portfolio (the new premia being present due to deviations from purchasing power parity). This is how, for example, we have the notion of an "international" CAPM versus a "classic" CAPM. The paper looks at testing an international APM in conditional form i.e. model for expected return conditional on current knowledge on interest rates, equity prices and so forth. Conditional expectation is critical here.