FRM P2, Market Risk Measurement, pages 4-5 (from Kevin Dowd's Measuring Market Risk, second edition)

[mkabbi]

I am preparing for the FRM and was reading Chapter 3 of the Market Risk book from Kevin Dowd's Measuring Market Risk, second edition.

On pages 4-5 (pages 53-55 in Kevin Dowd's book), the author discuss profit and loss data and compares arithmetic and geometric returns.

The author implied arithmetic returns give results dependent on a reference currency. However, according to the formulas, the units of currency cancel for both arithmetic and geometric returns. I calculated an exchange rate for a hypothetical problem and the arithmetic return was a percentage independent of currency, just as the geometric return is supposed to be.

If a person could clarify how arithmetic returns are different from geometric returns (with regards to currency), I'd appreciate it. I have attached pdfs of the FRM curriculum pages I am referring to.

 

[ShaktiRathore]

Hi,
Both geometric(GR) and Arithmetic return(AR) are dependent on bith the asset and currency returns,i mean there is no role of units of currency just the currency return.
If a% is asset return and c is currency return then,
AR=a+c (simply add currency and asset return for AR)while GR=(1+a)(1+c)-1=a+c+ac<>AR (conpound both returns for GR)therefore AR and GR are different based on the currenccy returns.
Thanks

 

[mkabbi]

ShaktiRathore, I'd appreciate it if you could look at the pdfs of the pages I uploaded. According to the message board, my pages haven't received any views yet. Thanks.

 

[ShaktiRathore]

Hi,
This sounds confusing to me i have never encounter such thing before really,As far as i can get the reference currency in case of geometric is the asset price itself so that if geometric returns are independent of the asset price(we cannot infer negative prices as in case of AR) this implies that the geometric do not depend on the reference currency(we cannot refer/get anything about asset price or reference currency value like negative prices etc.).
thanks

 

[Thomas Obitz]

I think what he means is that you do not have to bother which currency you use as the "reference" vs the "foreign" currency. With geometric returns, you can always just us the difference in interest rates. If you are using algorithmic returns, you get a completely different differential rate depending on whether you are using a USD/EUR or an EUR/USD pair.

Welcome to the big club of people who hate Dowd... the unclear language and the typos just drive me nuts.

;-)

 

[Thomas Obitz]

Oh, and before I forget: Try to look at the Dowd less as a scientific book and more as a collection of ideas he has collated. It can take you oodles of time of trying to understand what he actually means, the examples are full of mistakes, and the typesetting for GARP has added a few typos as well.

The value of the Dowd is that it is a very broad collection of methods on market risk measurement - if you are ever confronted with a slightly unusual requirement for a market risk measure, you have a good chance of finding something on this topic in his book (and a reference to literature which explains it properly...) - just my humble opinion.

 

[mkabbi]

If one of you could provide details with an example, I'd appreciate it.

 

[ShaktiRathore]

Hi
Suppose reference currency is usd so rate is usd/eur it changes from 1.2usd/eur to 1.5usd/eur so Geom ret=ln(1.5/1.2)=ln(1.25) and arith return=(1.5/1.2)-1=25%.
If instead reference currency is eur then rate changed from 1/1.2eur/usd to 1/1.5eur/usd then geom ret =ln(1.2/1.5) =-ln(1.25) which remains same in terms of magnitude changes only in sign,while aritth ret=(1.2/1.5)-1=-20% whch changes in magnitude so geom return is independent in terms of magnitude as Of which currency is used as reference currency usd or eur but arithmetic return do depend on which currency is used as referencr because it changes based on reference currency used usd or eur and gives a completely different picture.
Thanks