Capital Market Expectations: Calculating Std GIM

CFA Level III
#1

Problem inputs:

Std Dev US real Estate: 0.14

Covariance with GIM: 0.0075

Integration with GIM: 0.60

Sharpe GIM = 0.36

Rf = 3.1%

Expected return GIM = 7.2%

Cortez’s colleague Jason Grey notes that U.S. real estate is a partially segmented market. For this reason, Grey recommends using the Singer-Terhaar approach to the ICAPM and assumes a correlation of 0.39 between U.S. real estate and the GIM.

QUESTION: CALCULATE BETA US REAL ESTATE?

Answer: 0.58

The first step is to calculate Std GIM, I know that… but why :

Std GIM = RGIM - Rf / Sharpe GIM

but I can’t do:

Std GIM = COVi,GIM / Stdi * Corr i, GIM

???

Both seem valid formulas to me, what am I missing here?

Thanks

#2

where is this question?

#3

The question is in official CFA 2016 AM exam. It is called Block 3: Capital Market Expectations - CME.

But do you understand what I mean? It seems like you can pull a Std Dev GIM thru two different formulas that are both Legit with the provided inputs… But only if you do it via the sharpe formula it works and not via the Correl i, GIM = Cov i GIM / Stdv i * Std GIM.

#4

If I understand you correctly, you are trying to derive SDgim using the second formula. But the problem is you don’t have the correlation coefficient, so you must find SDgim via the Sharpe formula.

How are you going to find SDgim with the second formula without correlation between RE and GIM?

EDIT: Oh I see what you mean now. Ok ignore my post, the two formulas don’t reconcile. Using your second formula you’ll calculate a correlation of 0.47, as supposed to the 0.39 given

#5

@Licky

Yes exactly you understood the problem! This is a problem seen online on the CFAI website. Do you think there is a reason why it doesn’t reconcile based on the theory or you would chalk this is a mistake? I mean you have the inputs to plug in two diffirent formulas that could give you the Std Dev GIM.

#6

Don’t quote me on this - but I have a feeling this has something to do with how RE is a partially segmented market with GIM

#7

This is how i explain this one:

The covariance of 0.0075 is a data from the market.

The correlation of 0.39 is not an observation but an assumption ( it is stated: Grey[…] assumes a correlation of 0.39 between U.S. real estate and the GIM )

The questions states that the market are perfect : " assuming perfect markets"

This suggest that the assumption of a correlation of 0.39 is wrong and should not be used, the observed covariance of 0.0075 from the market should be used.

#8

get the sharpe of the market

(7.2 - 3.1)/std = 0.36

std = 0.1138

var = 0.1138^2 = 0.013

Beta = 0.0075/0.013 = 0.5769 (0.58)

??

#9

His problem is not to calculate Beta, it is to explain why COVi,GIM /( Stdi * Corr i, GIM) is not equal to (RGIM - Rf) / Sharpe GIM

#10

Because the correlation is assumed. And not the one derived from the COV output.

#11

Don’t stress too much about inconsistency of mock problems for most part they are not checked thoroughly:

http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91331248