Modeling a stock market using the S&P 500 index as an example
Keywords: log-normal distribution of wealth function, geometric random walk, Black-Scholes model, Bayes‘ classification, smoothing methods, AR models, signal-to-noise ratio
Improvement of return at reduced risk by means of stock market entry and exit signals
Keywords: risk-free interest yield, yield on stock, buy-and-hold strategy, market entry signal, market exit signal, trend, volatility, transaction costs, bull market, bear market, flat market, crash, index certificate, ETF, non-diversified stock
You have identified your risk-return range under the assumption of buying the “market“ (with ETFs, index certificates, or a basket of shares that represents the market) and applying a buy-and-hold strategy over a period of several years (except for profit taking and loss compensations to keep your stock proportion nearly constant). We now show that you can improve your personal risk-return ratio, i.e. you can either increase the yield on stock and at the same time lower the volatility of your stock account, or you can reduce the stock proportion without reducing your yield on stock. For this, you will need an answer to two main questions:
By modeling the stock market (applying a Kalman filter to an AR2-model for the trend), one gets signals for when to enter and exit the market that particularly help avoid long-lasting bear markets. The model is characterized by having only a few signals per year with a small rate of false alarms.