The effects of position sizing on expected return

In previous article we discussed about using expected return formula to make investment or trading decision (Read more here).  We also talked about the effects of psychology on expected return in another article (Read more here).  Today, we shall take a look on the effects of position sizing on expected return.

The effects of position sizing on expected return, to a certain extent, is highly affected by psychology.   It is the question of “How much is at stake?” that influenced the decision.

Example,

Consider two investments that generate the same expected return, but the minimum investment amount for both opportunities are $5,000 and $500,000 respectively, given that p=0.7, R_W=0.2, R_L=-0.1.

For $5,000 entry, the return and loss are +$1,000 and -$500.

For $500,000 entry, the return and loss are +$100,000 and -$50,000.

Which one will you choose?

There is no perfect answer for the above question.  It depends on the net worth, risk tolerance, investment duration and the goal of the investors.  High net worth and high risk tolerance investors may choose to invest in both; lower risk tolerance investors may ask for higher expected return on $500,000 investment as the amount at stake is higher.

Another example will be lottery jackpot.  The odd of winning the grand prize jackpot is about 1/40,000,000.  But due to the entry requirement is as low as $1 per entry, many people are willing to buy lottery ticket instead of invest their money in higher return assets.

Based on my observation, there is another effect of position sizing on investment decision.  Many investors did very well on their investment when their position size was small.  As the fund grows bigger, the precision of their investment decision tends to degrade.  It is very difficult to quantify but investors shall aware of this psychological effect.