Singer-Terhaar “perfect segmentation” formula

broadex · January 16, 2015, 10:06am

I understand the general fomula for equity risk premium driven from CAPM is: [(σ i) x (ρ i, M) x (Sharpe ratio]. And I perfectly understand that this applies to “ perfect integration”. However what I cant figure out is the rationale of the fomula for “perfect segmentation” of[(σ i) x Sharpe ratio GIM)] . I would think since the correlation with the GIM market is zero, the : [(σ i) x (zero) x (Sharpe ratio] = zero instead of [(σ i) x Sharpe ratio GIM)]. In other words how do we drive the “perfect segmentation” formula from CAPM?

cpk123 · January 16, 2015, 1:19pm

perfect segmentation => correlation with local market = 1 -> so it is [(σ i) x Sharpe ratio GIM)]

Market segmentation means that there are some meaningful impediments to capital movement across markets. Although many barriers to international capital flows have come down, some do per- sist and a number of asset markets are in practice at least partially segmented across national borders. The more a market is segmented, the more it is dominated by local investors.

When markets are segmented, two assets in different markets with identical risk characteristics may have different expected returns. If an asset in a segmented market appears undervalued to a nondomestic investor not considering barriers to capital mobility, after such barriers are considered, the investor may not actually be able to exploit the opportunity.

To address the task of estimating the risk premium for the case of complete mar- ket segmentation, we must first recognize that if a market is completely segmented, the market portfolio in Equations 9 and 10 must be identified as the individual local market. Because the individual market and the reference market portfolio are identi- cal, ρi,M in Equation 10 equals 1. (For example, if Canadian equities were a completely segmented market, the reference market portfolio and the individual market portfolio would each be a broad-based index for Canadian equities, and the correlation of such an index with itself would of course be 1.) The value of 1 for correlation is the max- imum value, so all else being equal, the risk premium for the completely segmented markets case is higher than that for the perfectly integrated markets case and equal to the amount shown in Equation 11:

RPi = σi * RPM / σM = σi * Sharpe Ratio GIM

broadex · January 16, 2015, 7:32pm

Thanks CPK. But reference market is the the Global Investable Market (GIM) and not the local market. Hence my argument that if there is prefect segementation, there is no correlation with the global market but 100% correlation with local market and my intuition is the fomula for driving prefect segementation should be [(σ i) x (zero) x (Sharpe ratio GIM] = zero; nothing to do with GIM but something to do with Sharpe ratio for a local market (which is ofcourse not mentioned in the model)???

cpk123 · January 17, 2015, 1:17am

When you are perfectly segmented - your GIM is also your local market (in a sense).

and even if it is not - this is from the book. I am not making this up.

broadex · January 17, 2015, 1:39pm

Well I think this model is bogus then. Thanks CPK - great as usual.

Unemployed · January 17, 2015, 7:59pm

How it is bogus? A bit oversimplified, however still consistent.

crosstheevil · February 15, 2016, 9:57am

I’m currently working on this, my question is: when market is completely segmented (dominated by local investors), risk premium is simply higher than when it is not completely segmented (i.e. ρ < 1) ?

MrSmart · February 15, 2016, 5:48pm

Obviously, yes.

crosstheevil · February 16, 2016, 7:20am

Thank you, so it really is that obvious …

MrSmart · February 16, 2016, 10:10am

You are multiplying by one, so the ERP will always be larger than if you are using a correlation <1, it’s simple mathematically. Conceptually, it’s not as obvious.