[R-SIG-Finance] Compute Portfolio Returns

[Brian G. Peterson]

Ravi S. Shankar wrote:
> But if in my portfolio I have cash and because of daily Mark to market 
> my cash position would reflect my earnings from my futures position. 
> Isn’t it sufficient to simply the compute the returns from Cash which 
> includes the changes from futures position?

I'm afraid when you used the word "returns" I made the assumption that 
you were speaking of percentage returns, and wanted the mechanics of 
computing these even on a hypothetical portfolio, not specifically on 
tracking change in value on a real portfolio.  So I'll try to operate in 
the context of a cash portfolio in this email.

Generally futures contracts,like any other derivatives contract will not 
"pay out" till expiration or sale of the contract. So I'm a bit confused 
when you speak of a change in your cash position as a result of the 
futures contract.  You may see a change in the amount of money you are 
able to invest in new purchases because of your margin agreement, but 
the actual cash value in your account should not change, although the 
market value of securities held obviously does change.  So I'll try to 
put this in  terms that I understand, and hopefully we can meet in the 
middle somewhere.

It is certainly possible to track the returns on a "live" portfolio by 
looking at the change in Mark to Market from day to day on all your 
positions, as long as there is no change in investment (cash deposited 
or withdrawn from the trading account).  This is the simplest way of 
tracking returns, to work from a net asset value (NAV) number on the 
portfolio.

If when you speak of your cash position, you are speaking of the Market 
Value of Securities held or the NAV of your account, then I think we are 
speaking of the same thing.

In very compact form:

NAV=Cash deposits+Market Value of Positions-Margin Balance

(adjusted for any inflows or outflows of capital invested from the 
trading account)

> Even for the forward position my cash would reflect it. If I have a 
> entered into a forward contract my cash would go up by the position 
> times the premium amount(?)

Your NAV will reflect it, yes.  While margin or securities may be put up 
as collateral for a forward contract, generally "cash" does not change 
hands until the expiration or sale of the contract.

Contrast this with a swap, where in many cases there are cash payments 
that happen throughout the life of the contract, depending of the terms 
of the contract...

> So I cant individually compute the returns from a future position or a 
> forward position without somehow including my cash position?

I spoke in my earlier email about computing the change in mark to market 
on the derivatives contracts into a returns calculation (as on a 
hypothetical portfolio).    This is, of course, somewhat more work than 
simply tracking the NAV of your account.

Hopefully we're all speaking about the same things now.  If there is 
still some confusion, hopefully we can clear it up in another round or two.

Regards,

   - Brian

> -----Original Message-----
> From: Brian G. Peterson [mailto:brian at braverock.com]
> Sent: Monday, January 28, 2008 4:04 PM
> To: Ravi S. Shankar
> Cc: r-sig-finance at stat.math.ethz.ch
> Subject: Re: [R-SIG-Finance] Compute Portfolio Returns
> 
>  
> 
> Ravi S. Shankar wrote:
> 
>>  I have in my portfolio cash, equity, futures and forwards. I need to
> 
>>  compute the returns of this portfolio.
> 
>>
> 
>>  If say I have cash of $100 and I buy only equity then my weights would
> 
>>  be the amount invested in each stock upon the total cash and the sum of
> 
>>  weights would add up to the total cash. The returns computation would be
> 
>>  a straightforward change in investment.
> 
>  
> 
> price * position size (in shares) = position value
> 
>  
> 
> You can, as you've noted, back into weights this way.
> 
>  
> 
>>  However, I need help in understanding how do I compute the returns (and
> 
>>  the associated weights) from a futures position and a forwards position.
> 
>>
> 
>>  a)       In the case of futures there would be a daily change in the
> 
>>  cash position due to Mark to market. So would the change in cash
> 
>>  position reflect the returns of futures position?
> 
>  
> 
> With the futures position you will always calculate the notional value
> 
> to mark to market. For most futures contracts this is the price * a
> 
> multiplier.
> 
>  
> 
> Change in notional value is your return (in currency units like US$ or EU).
> 
>  
> 
>>  b)       In case of forwards how do I compute the weights and the
> 
>>  corresponding returns? I cannot use the change in investment as there is
> 
>>  no initial investment and if I use the change in investment approach to
> 
>>  compute returns I would have infinite returns.
> 
>  
> 
> With a forward contract you would use the difference in price between
> 
> the forward contract face price and the current spot (market) price to
> 
> calculate the current "premium price" on the contract and use the change
> 
> in premium price to calculate your returns.
> 
>  
> 
>>  Any help would be appreciated (please let me know in case there is a
> 
>>  paper which I can refer to)
> 
>  
> 
> If you do not change your positions from your initial position, then
> 
> your starting weights do not change, but your actual weights will float
> 
> daily (or whatever your observation time is).
> 
>  
> 
> If you need the calculations for calculating returns from prices (or
> 
> price*multiplier notionals), look at function Return.calculate in
> 
> PerformanceAnalytics.  Or if you need the method for calculating
> 
> weighted returns from "prices" and starting weights, let me know.
> 
>  
> 
> Regards,
> 
>  
> 
>     - Brian
> 
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