# Performance Calcs - Can you help me resolve an argument

I’m having some heated arguments at work regarding how to calculate performance for our fund. Was hoping I could get some opinions from people on this forum. We’re a startup fund with no clients and still trying figure out some really basic stuff.

Basically what we’ve got is unit trust fund that tracks a stock index. On the back of that we’ve got a separate mandate that enables us to take option positions on behalf of clients.

The argument is how do we account for the option premium and return in the performance calcs?

There are 2 arguments being debated using an analogy of investment in a house and buying home insurance premium to calculate performance returns.

So pretend you buy a house for \$1M and you also buy insurance for \$300K (big number for example purposes). A few years later you sell the house for \$2M.

Argument 1:

You made \$1M profit on the house, but had \$300K expense, so your performance is ( (\$2M - \$1M - \$300K) / \$1M ) = 70%

Argument 2:

Your initial investment was \$1.3M (\$1M + \$300K), and at the end you walked away with \$2M, so your performance is (\$2M - \$1M - \$300K) / \$1.3M = 54%

I’m arguing for choice 2 but my boss (who’s got 15+ years derivatives trading experience) is saying that you can’t treat options in this way. He’s saying that the option premiums shouldn’t considered like upfront capital and that you should only be looking at the mark-to-market PnL on these for performance calcs (i.e not include premium in the denominator). One argument he is saying also which rings true is that if you only sell options (i.e. receive premium), then how would you calculate PnL (i.e. you’re exposing yourself to risk but haven’t put any money down except for margin).

The way I see it, you had to outlay \$1.3M and you got back \$2M, so the \$1.3M should be the denominator in your calcs instead of only \$1M.

Does anyone have any experience or opinions on this? I can see an argument for his method, but mine seems perfectly logical as well, but surely there must only be one correct way to do this.

Btw – does GIPS cover this kind of thing? Should I be looking there or is that for something completely different? I’ve only done L1 on it which is pretty brief.

Tink yo boss is right. It’s been years since I’ve done performance analysis.

cleverku, your example of comparing option premiums to home insurance is flawed! This is the source of your confusion.

If you buy a \$1M house plus \$0.3M in insurance, where did that \$0.3M come from? You must have had \$1.3M to begin with, assuming you did not borrow money. This is why method 2 makes sense for the house example.

If you have a \$1M porfolio and pay \$0.3M in option premium, you probably took that \$0.3M from your original capital. Hence, your base capital is still \$1 million. So, method 1 is correct for options.

Ohai, the overlay strategy that we have is going to be a seperate mandate to the fund.

So the client would give us an initial investement (\$1M to buy the house), and then we have an agreement with them that we can draw funds from them to enter an option strategy (the \$0.3M insurance). So they don’t actually know what their base capital is going to be when they initially give us funds (depends on options market at the time we are setting the trade). We give them a rough idea only (i.e. somewhere between \$1.2M and \$1.4M).

So my argument is that we need to calculate performance based on whatever the house and the insurance cost at the initial time, not simply based on the house. My boss disagrees with this.

Correct me if I’m wrong, but based on the mandate info I’ve given you, would you now agree that method 2 is correct?

Rule # 1 - The boss is always right.

Rule # 2 - If the boss is wrong, see rule # 1.

in jest.

I agree with method 1, your 300k is similar to sunk cost, you can’t grow that as capital

When you buy insurance and don’t use it, you can’t treat that as an investment.

^ also, in L3 GIPS there is something similar to your situation, look under the GIPS real estate section where it calculates the income and capital return

Ok. Thanks for clarifying. I’m thinking now that your base capital needs to be whatever money you take from the client. The client only knows that they gave you \$X dollars at inception and receive \$Y at maturity. From the client’s perspective, it doesn’t seem like any calculation other than (Y-X)/X should make sense.

If you pull in \$300k of client money in addition to the \$1M, it seems pretty clear to me that you used \$1.3M of their capital.

Your boss’s example of selling options would use a base of \$1M. If you sell options and receive \$300k in premium, your base capital is still \$1M, since you did not ask the client for more money.

Anyway, this is what makes sense to me conceptually. Not sure if there is an industry standard calculation to use. Also, note that this ignores timing of cash flows and assumes all client capital is contributed at inception.

I’m not entirely sure what the correct answer is for GIPS/performance, since I learned it for the exam and then forgot a lot of it. However, I would say that from a portfolio manager’s perspective it can be tricky to think about the returns of leveraged investments. For isntance in this paper:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1675067

the author argues that it can make sense to use the strike price of an option, its underlying value, or the options dollar-delta as the basis in the return calculation.

For options, I tend to think of return in terms of hypothetical dollar notional. For instance if you have 100 options on a stock worth \$500, the implied notional would be \$50,000. If at the time of the options trade, you plotted a return diagram, this implied notional would have the same dimension of return with \$50,000 of stock.

However, I can see why someone would use another calculation method.

If you’re buying puts, I have to agree with the OP. Whatever you spent/layed out should be included in the demoninator.

If you’re selling options and have a \$1m position in an Index, then that’s added to the profit, if they expire out of the money, that is.

But they’re in the money and you need \$300k to pay your counterparty, if you sell part of the index position to cover the loss, \$1m stays in the denominator… if you call down an additional \$300k from your clients, then the denominator becomes \$1.3m.