# Do you think only market experts can make money? Then think again!!

You might have always heard that low risk levels are associated with low potential returns and high levels of risk are associated with high potential returns.

There is a possibility that a person even while holding less risk can achieve high returns

Wondering how is that possible???

Yes, it is !!

Let solve this puzzle with the help of an experiment using coin flips and probabilities:
We assume that we are not a market expert and we may exit from our trade in profit or loss with 50-50% chances. Same is the situation in betting for head or tail by flipping a coin.
Therefore we consider betting on the flip of the coin to be similar to investing in stock market. But with a bit of optimism, we believe probability of Head = 0.51 and probability of tail = 0.49.

We have with us \$1000 and for every Head we win 100%, Tail we lose 100%.

We have two choices

1. we can play 1 bet of \$1000

2. we can simultaneously play 1000 bets of \$1 each

Which one would you opt for? Why?

Let’s find out an optimal solution to it …

Calculation of Reward
Single bet : 0.51* \$1000 + 0.49* (-\$1000) = \$20
Multiple bets: 1000 * (0.51* \$1 + 0.49* (-\$1)) = \$20

We can now say from the above calculation that the expected reward in both the cases is the same i.e. \$20 in both the cases.
Hence we hold the same rewards. But what about Risk? Should it be same or different?

Let’s work on measuring the Risk associated with each of them
Risk Measure 1: Probability to loose everything
Single bet: Probability to loose everything 49%
Multiple bets: Probability to loose everything= 0.49 X 0.49 X 0.49 ……0.49= 0.49^1000(very small)

Risk Measure 2: Standard Deviation
Single bet: computing stdev(1000,0,0,0,0,0,0…… )= \$31.62
Multiple bets: computing stdev(1,-1,1,-1,1,1…..-1)= \$1

Reward/Risk Ratio:
Single bet: Reward/Risk = \$20/\$31.62=\$0.63.
Multiple bets: Reward/Risk = \$20/\$1=\$20.

Isn’t there is a big difference!! We achieved similar rewards with significantly less risk.

Hence its always better to invest small amount with more number of bets rather than single bet with big amount. This helps in reducing your risk of losing entire amount at once and get better returns too.

(Source: Dr. Tucker Balch, Georgia Tech University)