# Stock Market Returns Are Almost Never Realized Returns

Unless one is fully invested in a single stock or ETF, portfolio returns depend on allocation. In the case of trading, returns depend in addition on risk parameters. Although this sounds trivial, some economists and bloggers do not seem to understand it. I hope the example will prove useful.

If there are N securities in a portfolio with equal dollar allocation, then market returns are scaled by this number. If a stock rises 10% for example and there are 10 stocks in the portfolio, the portfolio gain is 1%. This is obvious and most understand it.

With trading though the situation is a bit more complicated. There are many bloggers who have never actually traded. It is often obvious from their articles that they do not have a clear understanding of risk management and position sizing and how that affects account returns.

Most traders, especially the short-term types, use stops and size positions accordingly. They also trade a few different N markets for diversification purposes. If for simplicity we assume equal allocation of account equity to these N markets and a stop S for each trade, then the actual return is given by the following formula:

Account return = 100 × R × (Ps – Pb)/ (S × N)        (1)

where R is the risk percent on net equity and Ps, Pb and the sell and buy prices.

Let us look at a specific signal from our premium report. A long signal in AAPL with entry at 121.15 on a stop was triggered on January 25 last month. The target was at 124.85 and the stop was placed at 117.85. The exit was triggered on February 1 at 127.03 due to an opening gap. The market gain from the entry to exit was 4.85%.  The details are shown in the chart below.

If we assume equal allocation to three positions maximum and 2% risk on net equity, then the actual account return given by formula (1) is calculated as follows

Account return 100 × 0.02 × (127.03 – 121.15) /[(121.15 – 117.85) × 3] = 1.19%

Therefore, although the market return based on entry and exit was 4.85%, the account realized a modest gain of 1.19%.

The actual account gain is directly proportional to risk percent and inversely proportional to number of positions for same trade characteristics. We could get market return if we increased the risk percent to about 8.15% but in this case we would also increase the risk of ruin. Note that with a risk percent of about 8%, a trader is ruined for all practical purposes after about six losing trades because a loss of more than 40% is almost never recoverable in practice. For this reason the risk percent must be kept as low as possible and many recommend it is never greater than 2%.

The conclusion is that market returns shown in blogs and social media posts are never achieved in practice, as real traders know from experience.

If you have any questions or comments, happy to connect on Twitter: @mikeharrisNY