# Singer-Terhaar market segmentation q

Greetings boys and girls. lovely friday night in nyc, eerily familiar feeling of being UTTERLY LEFT OUT of all living things in the universe… sigh. here is my question. under Singer-Terhaar, for segmented markets, we assume the correlation of a market w. the GIM = 1. why is that? shouldn’t it be zero??? To figure out the E(Rm) for a partially integrated market A, we take a weighted average of the expected returns under full integration v. full segmentation, as follows: 1) 100% integrated: using the correlation of market A w. GIM s.t. E(RP) = correlation factor x st dev of market A x GIM Sharpe and 2) 100% segmented: using assumed correlation factor of 1 = st dev market A x GIM Sharpe but that doesn’t make sense! if the market is fully segmented, shouldn’t its correlation w. GIM Sharpe be zero, not 1? can anyone please explain?

The index that you are measuring correlation with is the local market index in the case of segmented markets (the “global” portfolio is really just the local market portfolio). The reason the correlation is 1 is because there is no impact from other markets, as it is fully segmented. It doesn’t explicitly state it for the integrated markets, but i would have to think the global portfolio is actually a true global portfolio, when you calculate integrated market equity risk premia. I think you are comparing two different benchmarks, local market for segmented, global market for integrated.

When segmented there is ONE market. You are comparing the market to itself. The correlation of any market to itself is 1. Does that make sense to you ?

zoya, Agree this is Seriously confusing. After June I am planning to research this and write a paper but will need a name to combine with mine to sound more impressive than Singer-Terhaar. Let’s do zoya-jbaphna model? I promise I will run with correlation of zero. BUT prior to June though let’s promise to run with correlation 1 JD

I think, they should have used another word for this. In the whole field of finance, including discussions on emerging markets investing etc., “segmented” is just a proxy for low correlation.

I had trouble with this too. Like MarkCFAIL’S explanation as the market portfolio now being the local market. thanks and moving on.

I, too, like the explanation that when dealing with segmented market, we have correlation of 1 because we’re measuring against local market. Problem with this is that in all the questions i’ve seen we are only given one GIM Sharpe, and we use the same GIM Sharpe in BOTH of the components that we weight when we take a weighted average of the expected returns under full integration v. full segmentation see, the Schweser example on page 93 in SS6 and yes, would be happy to work on the zoya-jbaphna update!

also, please see example on page 49-50 in Vol. 3 check to see that for the integrated case, we use the integration factor for the segmentated case, we DROP the integration factor, but STILL measure against the SAME GIM Sharpe how can we use an integration factor of 1 to measure segmented market? I’d understand if we had two GIM Sharpes: one for global GIM, the other for the local market but we’re using the same GIM Sharpe of .28 for all calculations

I would assume that this is a simplifying assumption made by the CFAI. Lot of information to cover.

Zoya, I did notice this when I reviewed the Schweser and almost mentioned it last night but I was tired and wanted to just move on. It is the only piece of the puzzle that doesn’t add up, and I wasn’t sure if the error was particular to Schweser but you mention it is in the curriculum the same way (same sharpe for both) above, right? Unfortunately I think we are just going to have to think inside of the box the CFAI wants us to think inside of, for these problems. As a matter of logic, I agree that it makes no sense to imply the sharpe ratio is the same (which implies the global portfolio is the same, or its an awful big coincidence that the local and global are the same sharpe).

GIM, as its name suggests, is the global market. Hence, whether your particular market is segmented or integrated should not make a big difference in the GIM Sharpe Ratio, I think. This especially hold if the market in question is an emerging market. I think this is why they did not mention that issue.

Yes, but the point is that the Schweser flat out says that the relevant “global market portfolio” is the local market, for segmented markets. I haven’t read CFAI’s version, but I would think it is similar given Zoya’s comment above. The fact that they use the same sharpe implies that there is no difference in the relevant global portfolio, when in fact there is. A correlation of 1 would only make sense if the relevant portfolio is in fact the local (for segmented), because if it is a global portfolio and the market is segmented, there should be a very low or negative correlation.

Mark Both the Schweser and CFAI treatment are the same: the same GIM Sharpe is used for both integrated and segmented calculations. I guess I too will just accept this and move on, but one WOULD think that a “perfectly” segmented portfolio would have a correlation of 1 ONLY to the local segmented market, and NOT to the GIM Sharpe.

It makes sense that we use the same Sharpe for the GIM, since it is one global market. This piece from the CFAI curriculum might help: (equation 10 is: RPasset = SD of asset x correlation of asset and world market x sharpe ratio of world market) pg 43, Volume 3 "Equation 10 requires a market Sharpe ratio estimate. Singer and Terhaar (1997, pp. 44–52) describe a complete analysis for estimating it. As of the date of their analysis, 1997, they recommended a value of 0.30 (a 0.30 percent return per 1 percent of compensated risk). Goodall, Manzini, and Rose (1999, pp. 4–10) revisited this issue on the basis of different macro models and recom- mended a value of 0.28. For this exposition, we adopt a value of 0.28. In fact, the Sharpe ratio of the global market could change over time with changing global economic fundamentals. (Level III Volume 3 Capital Market Expectations, Market Valuation, and Asset Allocation, 4th Edition. Pearson Learning Solutions p. 44). "

Celtics, regardless of what they say, it doesn’t make sense to imply that a fully SEGMENTED market, which would have little or ZERO correlation to a global portfolio as it is segmented off from other countries in terms of trade, cross holdings of sovereign debt, multinational corps, etc - so it’s only concern would be itself. If the portfolio is indeed a “global market portfolio”, then i don’t buy that the correlation to the global market is 1 for a market that has no ties to globalization, how would that be? I would think the more integrated you are, the closer to 1, and vice versa. The only logical explanation as you are dealing with two different portfolios, whether the CFAIL says it or not - one being the local port (for segmented), and one being the global (integrated). If it is global for both, then the correlations are wrong.

Footnote on page 45. “For simplicity, we are assuming that the Sharpe ratios of the GIM and the local market portfolio are the same”

jmac01 Wrote: ------------------------------------------------------- > Footnote on page 45. “For simplicity, we are > assuming that the Sharpe ratios of the GIM and the > local market portfolio are the same” that makes sense now Thanks jmac !

then its settled. they are NOT the same portfolio. Thanks.

An intuitive way to understand this is if you have totally segmented markets- the correlation number you use is 1- this will give you a higher risk premium. If you have integrated markets- you use a correlation which by definition will be less than 1. This will give you a lower risk premium, as long as the sharpe and standard deviation remain equal in both equations.

bump

Anyone else having problem with understanding their approach?