Doc Maher examines Anyway's Finish High trade and expected return.
The brave knight Anyway has continued his option journey into the land of FROs. Click here for a treasure trove of FRO resources.
So you jumped right in to try your hand at FROs! I saw your trade note about buying the GE May 32 Finish High FRO. I have a brief comment for you.
Here it is:
I think you paid too much!
Got your attention?
The explanation involves calculating expected return. The short version - when calculating the expected return, I come up with a negative number or a loss of $0.12. What this means is that on average this trade is expected to show a loss of $12. If the price of the FRO was lower or GE was higher (you stated it was around 32.20) it might have shown a positive return on average.
The fact that the expected return is a negative is not all that bad. Lots of trades, especially simple ones like this are going to have a negative expected return because the people selling them to you don't want you to have a statistical advantage. So how do you make money? Well the statistics are based on the stock moving "randomly" within ranges defined by how much it moved in the past. If you have reason to believe that the stock is not going to move "randomly" i.e. maybe you think it's trending, then you may have an advantage.
Since the term "expected return" has been introduced in earlier postings I think it's helpful to understand what it is and how it's calculated. FROs offer about as simple a case as we are likely to come across. The explanation is a little long, but I think you'll get it in the end.
You stated that the trade was made on 5/12 and that GE was at approximately $32.20. You paid $0.70 for a May 32 Finish High FRO.
This means that if the final GE VWAP is over $32 you will get $1. (The final value is called the Amex FRO Settlement Index and will be determined by 6pm on expiration Friday.) However you paid $0.70 so you will net $0.30. If it ends below the $32 VWAP the FRO is worthless and you net a loss of the $0.70 that you paid for it.
The question I want to explore is how good a deal is this? We stand to gain $0.30 but lose $0.70, which is not a good risk to reward ratio. However there is a better chance that we will get the $0.30 than lose the $0.70, but how much better? Is the risk worth taking?
So let's analyze what one might expect on average from this trade, if we made a large number of trades. To do that we have to figure out what the chances are of GE being above $32 on 5/16. The VWAP is going to confuse things a bit so let's just look at the chance of GE being over $32 on 5/16. I am also ignoring commissions here.
Here is a calculation that can be done to estimate the chances. Before I start let me say that there are a number of assumptions that are part of this calculation, any of which may be argued. The first assumption is that GE is going to act randomly and that its prices are going to fall into what is called a Normal Distribution over time. Sometimes this is called a random walk. It means that the stock moves randomly according to the assumed "Normal Distribution". This sort of assumption is not unusual and is the basis of most statistics. More complex models may use other distributions.
On 5/12 when you entered the trade, a Normal Distribution for GE prices might look like this.
Click here for a larger image.
The closer a potential 5/16 closing price is to the starting price of $32.20, the more likely that it will occur. The farther away the price, the less likely it will be. The most likely price is $32.20. There is almost no chance that the price could get down to $30 or above $34 for this distribution.
We want the price to stay above $32. All of the area under the curve to the right of $32 represents the chance that GE will be above $32 on 5/16. All of the area to the left represents the chance that GE will be below $32. Here's a picture.
Click here for a larger image.
We can see that the area on the "greater than" $32 side is larger than the area on the "less than" $32 side. So we know that it is more likely that GE will end up above $32, but how much more likely?
To figure that out we have to do a little math, but I promise it won't be that hard and I'll do all the numbers. To start we need to figure out a couple of things about the curve. First, what is the mean or the highest point? We already know that because we want the distribution to be centered around the current price or $32.20 (as of the trade entry). Second, we need to figure out the standard deviation of GE's prices. There are a number of ways that we can estimate that. An easy formula to use is:
Click here for a larger image.
Looks confusing but it's not. The time in question is one week, so we have 52 weeks in one annual period. If we were interested in a month it would be 12 etc.
We know the price is $32.20, the question is what should we use for the Volatility? If we use the Historical Volatility we are expecting GE to continue to act as it did in the past. If we use the Implied Volatility we are using the "projected movement". In this case let's stick to the Historical Volatility. So from the below chart:
Click here for a larger image.
We can see that the HV over the last 30 days is 43.74%. This is rather misleading I think. Let's look at the GE chart:
Click here for a larger image.
The big gap is overly influencing the HV. We can either use a shorter HV like 20 days which doesn't include the gap or use the IV which is forward looking. The IV is approximately 22% from the chart and the 20 day HV is 15.3% which I found elsewhere.
Let's calculate Standard Deviation using 22% IV, one week of time, and a starting price of $32.20.
Click here for a larger image.
This means that there is about a 68% chance that GE will not move more than $0.98 up or down from the starting point in the time we are looking at. In this case we don't care if it moves up, we only need to figure out the chance that it will move down more than $0.20.
So we need to figure out how many standard deviations $32.00 is from $32.20. We have $.20 of allowed movement divided by $0.98. This equals 0.20 standard deviations. Knowing this, I can use a table to determine the probability that GE will stay above $32.00, which turns out to be 57.93%. These tables can be found in many books and also on the internet, not that you were going to try this at home.
So what does this mean? It means that when you started this trade you had a 58% chance that GE would stay above $32 and a 42% chance that it would go below $32.
Another way to say the same this is you have a 58% chance of making $0.30 and a 48% chance of losing $0.70.
Here are the final calculations to determine the expected return.
$0.30 x .58 = $0.17 gain
$0.70 x .42 = $0.29 loss
The Total "expected gain" is the difference, which is -$0.12.
So if GE is truly moving randomly and looking at the chart that's probably a good approximation for the next week, we would expect on average to lose $0.12 on every trade. Of course some would make $0.30 and some we would lose $0.70 but when we averaged all of the outcomes, we would expect that we lost an average of $0.12.
What all this tells me is that the price you paid for the FRO is too high considering how close GE was to the ‘strike' to make money on average. This is also dependent on what we use for the volatility. Looking at the chart, 15% is probably a better indication and that would have changed the number somewhat. The odds of staying above $32 would have gone up slightly to 62%.
The random movement assumption is at the heart of all "expected return" calculations. Much of the time we don't believe that the stock is moving randomly; we think it's in an up trend or a down trend or we see resistance or something. So a negative expected return may not be that important to you. However in this case where the stock appears to be moving sideways, I think it's a good thing to look at.
This was a relatively simple expected return calculation because it involved one option and there were only two possible returns. In most situations these calculations are much more involved. However for the FRO they can be done by hand or with a spreadsheet.
Anyone interested in doing or understanding expected return calculations can ask for more information or research further. For most situations you will want a software package to do the calculation if you are interested in knowing the "expected return" for a particular trade.
I hope this hasn't been too confusing and that it helps you understand what expected return is and how we might use it when looking at FROs.
"Income Trader"
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This comment and any market data included here were completed on 5/13/08.
Options involve risk and are not suitable for all investors.
Please read Characteristics and Risks of Standardized Options.
While implied volatility represents the consensus of the marketplace as to the future level of stock price volatility or probability of reaching a specific price point there is no guarantee that this forecast will be correct.
Any strategies discussed and examples using actual securities and price data are for educational and illustrative purposes only and do not imply a recommendation or solicitation to buy or sell a particular security or to engage in any particular investment strategy. In reading content in the Community, you may gain ideas about when, where, and how to invest your money. Although you may discover new ideas or rationale that may be compelling, you must ultimately decide whether or not to put your own money at risk. Consider the following when making an investment decision: your financial and tax situation, your risk profile, and transaction costs.
Jonathan F. Maher, PhD has a professional business relationship with TradeKing.
