# Binary Options Returns – Good or Bad?

17th April, 2012 - Posted by in Binary Options Articles

#### Binary Options Returns Good or Bad?

Binary options returns good or bad? To better answer this question one must consider the return on offer, the expected return, plus the competing opportunities.

Game of Chance
Consider  the game of Heads or Tails where two contestants (the house and the customer) toss a coin for, say, a \$1 stake. Assuming some physical quirk in the coin does not exist, e.g. it can balance on its edge, or a subtle form of cheating is eliminated, then the coin has a 50% chance of being a head and a 50% chance of being a tail. The expected return is:

House Expected Return     =     ((1-Probability of winning) x (1-Rebate)

- (Probability of losing x Return)) x Stake

which in the case of the house paying out 100% return is:

House Expected Return    =     ((1 – 50%) x (1-Rebate)) – (50% x 100%) x \$1

=     50¢ – 50¢ = \$0

So, with the Return set at 100% and Rebate at 0%  the expected return is \$0.

If the client winning return was 90% but the client forfeits 100% of the stake if they lose, i.e. rebate = 0% then:

House Expected Return    =    ((1 – 50%) x (1-Rebate) – (50% x 90%)) x \$1

=     (50 – 45) x \$1 = 5¢ or 5%

Client Expected Return    =    ((50% x 90%) – (1 – 50%) x (1-Rebate)) x \$1

=     (45 – 50) x \$1 = -5¢ or -5%

which is basically stating that the client would lose 5¢ for each \$1 they bet.

If the rebate were set at 10% with client winning return 90% then:

House Expected Return    =    ((1 – 50%) x (1-10%) – (50% x 90%)) x \$1

=     (45 – 45) x \$1 = 0¢ or 0%

Client Expected Return    =    ((50% x 90%) – (1 – 50%) x (1-10%)) x \$1

=     (45 – 45) x \$1 = 0¢ or 0%

which is basically stating that the client and house would both scratch.

The coin-tossers are playing a game of chance where the more the coin is tossed, the more the number of heads will converge on 50% of the total, and therefore, of course, the total number of tails will converge on 50% of the total. For example:
If ten coins are tossed the outcome maybe 6 heads and 4 tails, i.e. 60% heads, 40% tails.
If 100 coins are tossed the total number of heads is 55 and tails 45, i.e. 55% heads, 45% tails.
If 1000 coins are now tossed the percentages might now be 52% and 48%.
If the coins were tossed an infinite number of times then the numbers of heads will likely be 50% and so tails will too be 50%.

Game of skill

If we consider that the Efficient Market Theory (EMT) is valid we are, in effect, saying that at any one time there is a 50:50 chance of the market going either up or down. But this overlooks some pertinent facts, one of which being that binary options traders are involved in a game of skill, a game that millions upon millions of people are playing around the world each day.

The skill element means that it is feasible that a trader can call the market right more often than the efficient market theory’s 50% of the time. Why is this? EMT makes the assumption that ALL the possible information in the world is known by ALL interested parties that may want to buy and/or sell the market. This means that an equilibrium position is attained where 50% of the market by weight of money believes the market is going up, while 50% by weight of money believes the market is going down.

So, let us assume a return of 85%, a 0% rebate and the client believes that they get the market right 68% of the time. Then:

Client’s Expected Return     =     ((68% x 85%) – (1 – 68%) x (1-0%)) x \$1

=     (0.578 – 0.32) x \$1 = 25.8¢ or 25.8%

If the client believes they get the market right 60% of the time their expected return becomes:

Client’s Expected Return     =     ((60% x 85%) – (1 – 60%) x (1-0%)) x \$1

=     (0.51 – 0.40) x \$1 = 11¢ or 11%

The following tables offer a range of platform returns and clients view of their own probability of calling the market correctly to provide a table of expected returns. The rebate for the table and following graph are in the title.
1. The bottom axis is the client’s own perception of their probability of winning.
2. The Platform Return is the return offered by the binary platform operator on the client winning.
3. Rebate is the rebate offered by the binary platform operator for a losing trade
4. The vertical axis represents the client’s Expected Return.

EXPECTED RETURNS : Rebate = 0%
Trader's View of Probability of Winning
50%60%70%80%90%100%
Platform Return = 60%-20.0%-4.0%12.0%28.0%44.0%60.0%
Platform Return = 70%-15.0%2.0%19.0%36.0%53.0%70.0%
Platform Return = 80%-10.0%8.0%26.0%44.0%62.0%80.0%
Platform Return = 90%-5.0%14.0%33.0%52.0%71.0%90.0%
Platform Return = 100%0.0%20.0%40.0%60.0%80.0%100.0%

Fig.1 – Expected Returns of an Over/Under Trader with 0% Rebate

EXPECTED RETURNS : Rebate = 5%
Trader's View of Probability of Winning
50%60%70%80%90%100%
Platform Return = 60%-17.5%-2.0%13.5%29.0%44.5%60.0%
Platform Return = 70%-12.5%4.0%20.5%37.0%53.5%70.0%
Platform Return = 80%-7.5%10.0%27.5%45.0%62.5%80.0%
Platform Return = 90%-2.5%16.0%34.5%53.0%71.5%90.0%
Platform Return = 100%2.5%22.0%41.5%61.0%80.5%100.0%

Fig.2 – Expected Returns of an Over/Under Trader with 5% Rebate

EXPECTED RETURNS : Rebate = 10%
Trader's View of Probability of Winning
50%60%70%80%90%100%
Platform Return = 60%-15.0%0.0%15.0%30.0%45.0%60.0%
Platform Return = 70%-10.0%6.0%22.0%38.0%54.0%70.0%
Platform Return = 80%-5.0%12.0%29.0%46.0%63.0%80.0%
Platform Return = 90%0.0%18.0%36.0%54.0%72.0%90.0%
Platform Return = 100%5.0%24.0%43.0%62.0%81.0%100.0%

Fig.3 – Expected Returns of an Over/Under Trader with 10% Rebate

EXPECTED RETURNS : Rebate = 15%
Trader's View of Probability of Winning
50%60%70%80%90%100%
Platform Return = 60%-12.5%2.0%16.5%31.0%45.5%60.0%
Platform Return = 70%-7.5%8.0%23.5%39.0%54.5%70.0%
Platform Return = 80%-2.5%14.0%30.5%47.0%63.5%80.0%
Platform Return = 90%2.5%20.0%37.5%55.0%72.5%90.0%
Platform Return = 100%7.5%26.0%44.5%63.0%81.5%100.0%

Fig.4 – Expected Returns of an Over/Under Trader with 15% Rebate

It is clear that the client’s own perception of their own ability in this ‘Game of Skill’ is critical to the hypothesis ‘Binary Options Returns – Good or Bad?’. If the client is accurate in their own understanding of how often they call the market correctly then the client is capable of positioning themselves along the bottom axis and looking at the rebates and platform returns on offer to decide whether this is a profitable exercise, whether a ‘good return’ is available to them.

But yet again another element is omitted: people recognise that smoking cigarettes does not offer a good financial return but they still do it. Why? They enjoy it. Trading binary options may well offer an intangible benefit, enjoyment, which does not fit into the above analysis……………..