S&P 500  2,725.27 (+0.51%)

# Tutorial

The purpose of this web-site is to estimate future returns of stock market indices by modelling and simulating their underlying economics.

A stock market index is a collection of stocks of different companies which may be considered a single large conglomerate so its underlying economics can be modelled as a single company.

## Equity Growth Model

Most companies require an increase in assets in order to increase their revenue and earnings, for example, a company may require additional factories to increase production.

Assets are funded by equity and liabilities so an increase in assets must be matched by an increase in equity and liabilities. A company may increase its equity by retaining earnings which means that fewer earnings can be paid out to shareholders.

The accumulation of equity from retained earnings is modelled here and used to forecast the future equity, earnings and dividends. The basic equity growth model is detailed in [1].

## Monte Carlo Simulation

Using this model to forecast the future equity, earnings and dividends requires knowledge of the future Return on Equity (ROE) and fraction of earnings being retained. Historically these numbers have varied as shown in the statistics.

The historical data for the ROE and retained earnings is used in Monte Carlo simulation to estimate the probability distributions for the future equity, earnings and dividends.

The historical data for the P/Book ratio is used in Monte Carlo simulation with the simulated equity to estimate the probability distribution for the future price.

## Value Yield

The value yield is the annualized rate of return an investor would get from buying shares at the current price and holding the shares for a given period. The value yield is useful in comparison to other available yields such as low-risk government bonds.

The investment return consists of dividends during the holding period and the selling price at the end of the holding period. For short holding periods the return is dominated by the selling price which is volatile so the value yield is also volatile. For long holding periods the return is dominated by the dividends which are more stable so the value yield is also more stable.

Formally, the value yield is the discount rate that makes the present value of the future dividends and selling price equal to the current price:

Price = Pricen/(1 + Value Yield)n + Σ Dividendt/(1 + Value Yield)t for t=1 to n

The value yield is often called the internal rate of return but that is a misnomer and may be confused with ROE.

## Limitations

There are several limitations of the equity growth model:

• The future is simulated from historical data which is assumed to recur indefinitely and in random order. Although the historical data covers a period with asset bubbles, economic crises, wars, etc., the future may hold vastly different scenarios which could significantly alter the economy.
• The future equity, earnings, dividends and price do not follow simple probability distributions in the near future but approach log-normal distributions in the distant future. The value yield distributions are not simple either but are somewhat centralized like normal distributions. For simplicity the mean and standard deviations are shown here.

## References

 [1] Monte Carlo Simulation in Financial Valuation Pedersen, M.E.H., Hvass Laboratories Report HL-1302, 2013