Basis Risk

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2^#

发表于 2011-7-11 19:08 | 只看该作者

Where are you seeing this?

Your understanding of basis risk seems accurate to me. (although there maybe other sources for basis risk other than interest rate risk, e.g. commodity futures will face basis risk due to quality, location, etc.)

Typically the futures will be close to spot as the contract is close to maturity, during that time the basis risk is naturally low; perhaps the text is not articulating time aspect?

Edited 1 time(s). Last edit at Sunday, May 1, 2011 at 08:42AM by jbaphna.

infinitybenzo

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发表于 2011-7-11 19:08 | 只看该作者

Moreover: It is said the basis is at any time: Ft - St
Why it is not Ft/St ?

Iginla2011

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发表于 2011-7-11 19:08 | 只看该作者

Imagine I have stocks in Switzerland for 100 CHF => portfolio value is 100* 5 = 500 USD
=>sell for 100 CHF of futures contract (eg. 100 contract of 1 CHF)

At time t:
Portfolio value = 100*10 = 1000 USD
Future value = 100 * (20 - 10) = 1000 USD
Total = 1000 - 1000 = 0 USD

You have right. The basis can't be Ft/St

If the basis were constant:
F0 = 10, S0 = 5, Ft = 20, St = 15

At time t:
Portfolio value = 100*15 = 1500 USD
Future value = 100 * (20 - 10) = 1000 USD
Total = 1500 - 1000 = 500 USD

To sum up, if perfectly hedged:

V*St - V(Ft-F0) = V * S0
....
Ft-St = F0-S0

The basis should be constant !

ll11

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发表于 2011-7-11 19:08 | 只看该作者

bern Wrote:
-------------------------------------------------------
> Imagine I have stocks in Switzerland for 100 CHF
> => portfolio value is 100* 5 = 500 USD
> =>sell for 100 CHF of futures contract (eg. 100
> contract of 1 CHF)
>
> At time t:
> Portfolio value = 100*10 = 1000 USD
> Future value = 100 * (20 - 10) = 1000 USD
> Total = 1000 - 1000 = 0 USD
>
> You have right. The basis can't be Ft/St
>
>
> If the basis were constant:
> F0 = 10, S0 = 5, Ft = 20, St = 15
>
> At time t:
> Portfolio value = 100*15 = 1500 USD
> Future value = 100 * (20 - 10) = 1000 USD
> Total = 1500 - 1000 = 500 USD
>
>
> To sum up, if perfectly hedged:
>
> V*St - V(Ft-F0) = V * S0
> ....
> Ft-St = F0-S0
>
> The basis should be constant !

I'm confused by your example.

Beginning portfolio is $500 or 100 CHF, right?
Sold 1 contract (100CHF @ $5/1CHF I'm assuming?)

Lay off the numbers for a minute. I don't see why you're trying to challenge the CFA material, where it clearly states that the basis can change, hence basis risk. They use the example of interest rate differentials to illustrate their case. If US risk free rate is 1% and the CHF risk free rate is 4%, will the basis always be 3%? No, because the US can raise rates at will. Swiss government can do the same.

What if these were oil futures? Let's say you need oil barrels in Texas, but the barrels linked to the contract are in Alaksa since there are no counterparties available that have oil in Texas. Or what if you're an airline that uses jet fuel as an input but there are no jet fuel contracts to hedge, so the closest thing available is oil. Sure seems like there's some basis risk there. The price of jet fuel could go up even if the price of oil stays the same.

NO EXCUSES

mar350

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发表于 2011-7-11 19:08 | 只看该作者

I was not trying to challenge the CFA material, but just saying that I finally understood the point thanks to your previous post (think in terms of $ and not %). So I showed a proof of my mistake with an example.
By saying "The basis should be constant ! " I wanted to say "The basis should be constant if we want not basis risk"

Edited 1 time(s). Last edit at Sunday, May 1, 2011 at 11:28AM by bern.

mcmc

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发表于 2011-7-11 19:08 | 只看该作者

bern Wrote:
-------------------------------------------------------
> By the way. In the CFAI volume 5 page 302 it is
> said that a contract with the same maturity as the
> investment has no basis risk.
> Do I understand well ? Because, if the basis is
> not 0 at time 0 and is 0 at time t (Future & Spot
> converge) there is basis risk, no ?

Basis risk is zero because futures price is expected to converge to spot price at maturity.

Windjammer

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发表于 2011-7-11 19:08 | 只看该作者

At initation, the basis = F0 - S0
At maturity, the basis = 0
=> the basis is not constant => there is basis risk, no ?

zwjy

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发表于 2011-7-11 19:08 | 只看该作者

bern

First a minor point basis is not F - S but it is S - F

More importantly, Futures price is expected to follow an expected path of convergence to spot, i.e the Value of (S0 - F0) is expected to diminish to zero when contract expires. The risk is that the Futures price deviates from this expected path. This risk is important as the Futures position may not be held till expiration.

If the basis reduced from (S0 - F0) to 0 exactly along expected path, then there is no basis risk. In other words the expected carry benefit, storage and financing costs experienced are exactly as expected when futures were priced at time 0.

Confusing?

aidebaobao

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发表于 2011-7-11 19:08 | 只看该作者

This chapter makes me crazy !!!

Let's use an example.

F0 = 10, S0 = 5, Ft = St = 15

At time 0:
Portfolio = 100 CHF = 500 USD

At time t:
Portfolio value = 100*15 = 1500 USD
Futures value = 100 * (15 - 10) = 500 USD
Total = 1500 - 500 = 1000 USD

1000 USD > 500 USD
Isn't it the result of basis risk that the final amount is not the same as the beginning one ?

Edited 1 time(s). Last edit at Sunday, May 1, 2011 at 03:12PM by bern.