P2.T8.405. Style analysis and market timing

[Nicole Seaman]

Questions:

405.1. Let the market timing score be equal to the proportion of correct forecasts of bull markets, P(1), plus the proportion of correct forecasts of bear markets, P(2), minus one; i.e., per score = P(1) + P(2) - 1.0. During the fourteen calendar years from 2000 to 2013, a market economist predicted a bear market for each of the first seven years, until 2006, then switched his view and predicted bull markets for the subsequent seven years. Below are displayed the actual returns for the market (using the S&P 500 as proxy) over the same fourteen years:

Which is nearest to the economist's market timing score?

a. Zero
b. 0.28
c. 0.35
d. 0.49


405.2. A portfolio manager is evaluated by a style analysis that compares her actively managed portfolio to the benchmark portfolio; aka, bogey. The benchmark portfolio invests in three components: 60.0% in the S&P 500 (the equity index), 30.0% in a Lehman Bond Index (the bond index), and 10.0% in a money market fund (the cash index). A portfolio passively invested in this bogey portfolio would have returned +4.0% over the period. The manager's actual portfolio components included 80.0% in equities, 10.0% in bonds, and 10.0% in cash. The manager's actual portfolio overperformed the bogey by 90 basis points (i.e., 4.9% actual portfolio return compared to a 4.0% bogey portfolio return):

If the excess return of +0.9% is decomposed into two components, asset allocation and security selection, what is the contribution to the excess return from asset allocation?

a. -0.20%
b. Zero
c. +0.40%
d. +0.75%


405.3. A portfolio manager is evaluated by a style analysis that compares her actively managed portfolio to the benchmark portfolio; aka, bogey. The benchmark portfolio invests in three components: 70.0% in the S&P 500 (the equity index), 20.0% in a Lehman Bond Index (the bond index), and 10.0% in a money market fund (the cash index). A portfolio passively invested in this bogey portfolio would have returned +7.4% over the period. The manager's actual portfolio components included 60.0% in equities, 20.0% in bonds, and 20.0% in cash. The manager's actual portfolio overperformed the bogey by 120 basis points (i.e., 8.6% actual portfolio return compared to a 7.4% bogey portfolio return):

If the excess return of +0.9% is decomposed into two components, asset allocation and security selection, what is the contribution to the excess return from security selection?

a. -0.80%
b. 0.80%
c. 1.30%
d. 2.00%

Answers here:

• In forum

 

[PBHAMIDIPATI]

The question reads bull for both the periods (up to 2006 and after). It should read 'bear' for first 7 years?

 

[David Harper CFA FRM]

Hi @PBHAMIDIPATI Yes, thank you! I fixed the text to read (and match the exhibit): "During the fourteen calendar years from 2000 to 2013, a market economist predicted a bear market for each of the first seven years, until 2006, then switched his view and predicted bull markets for the subsequent seven years."

+1 star (for contribution). This has not gone to PDF yet, so no pdf revision required ... thanks!

 

[FRMCAND]

Hi BT Team,
in 405.1 :
I do not understand if we have to compute the proportion of corrects forecasts of bear/bull markets over the seven or the fourteen years period.
I was comuting P(1) and P(2) over the overall period and having differents observations:
P(1) = 4/4 and P(2) = 7/10
score = P(1) + P(2) - 1 = 4/4+7/10-1= 0.7
in 405.2 :
contribution from asset allocation should be (80%-60%)*5.0% + (10%-30%)*3.0% + (10%-10%)*1.0% = - 0.40%
Thank you in advance for your attention.
Best Regards.

 

[David Harper CFA FRM]

Hi @FRMCAND Sorry, I can easily be wrong (both of these can be tricky), I am constantly making mistakes, but I don't see either of your points:

• You've swapped P(1) and P(2) which doesn't matter. But how do you get 4/4 bear markets; and how is that commuting over the entire observation, any case? There are four bear markets (negatives in red) and the economist correctly forecast three (on the left) but he missed the one in 2008, so he's 3/4 on the bear markets. There are 10 bull markets (i agree with your denominators) but he missed (predicted bear) on four of them (2003 to 2006), so he's 6/10 on bull markets. Bodie uses "the proportion of bull markets correctly forecast and the proportion of bear markets correctly forecast"
• Re 405.2, I agree (80%-60%)*5.0% + (10%-30%)*3.0% + (10%-10%)*1.0%, but that's +20%*5.0% + (-20%)*3.0% + 0 = +1.0% - 0.6% = 0.4%. Let me know if I missed something, thanks,

 

[cdbsmith]

Hi @FRMCAND Sorry, I can easily be wrong (both of these can be tricky), I am constantly making mistakes, but I don't see either of your points:

• You've swapped P(1) and P(2) which doesn't matter. But how do you get 4/4 bear markets; and how is that commuting over the entire observation, any case? There are four bear markets (negatives in red) and the economist correctly forecast three (on the left) but he missed the one in 2008, so he's 3/4 on the bear markets. There are 10 bull markets (i agree with your denominators) but he missed (predicted bear) on four of them (2003 to 2006), so he's 6/10 on bull markets. Bodie uses "the proportion of bull markets correctly forecast and the proportion of bear markets correctly forecast"
• Re 405.2, I agree (80%-60%)*5.0% + (10%-30%)*3.0% + (10%-10%)*1.0%, but that's +20%*5.0% + (-20%)*3.0% + 0 = +1.0% - 0.6% = 0.4%. Let me know if I missed something, thanks,

David,

I'm struggling with question 405.1:

Why doesn't P(1) = 3/7 and P(2) = 6/7? In other words, is P(1) equal the proportion of correct bear market forecasts to total actual bear market results, or the proportion of correct bear market forecasts to total bear market forecasts? Likewise, is P(2) equal the proportion of correct bull market forecasts to total actual bull market results, or the proportion of correct bull market forecasts to total bull market forecasts?

Thanks,

Charles

 

[FRMCAND]

Hi David,
don' t worry, this time I'm wrong !

• 405.1: now I get the correct interpretation for the market timing score. I was wrongly calculating the correct forcasts, because I took into account the overall underlying period of 14 years and not 7 years. In addition the question clearly states: "a market economist predicted a bear market for each of the first seven years, until 2006, then..." . So I have to stop at 2006 to compute the correct bear market predicted. Then, the economist's expectation for 2008 was a bull market, while the actual shows bear market.
• 405.3: I apoligize about the question and take your time for this, lost in very simple calculation, sorry.

Thank you very much,

 

[joacogimeno]

Hello, @cbdsmith:

P(1) = 3/7 because out of 7 years (periods), he correctly identified 3 of them as "bear years" = negative growth.
P(2) = 6/7 because out of 7 years (periods), he correctly identified 6 of them as "bull years" = positive growth

Thus, market timing score = 3/7 + 6/7 -1 = 3/7 + 6/7 - 7/7 = 2/7 = 0,28

EDIT: The answer on the forum seems to be different, but it explains it in a weird way: "P(1) = 6/10 correct bull forecasts, P(2) = 3/4 correct bear forecasts, such that score = 0.60 + 0.75 - 1.0 = 0.350."

¿6/10 correct bull forecasts? ¿3/4 correct bear forecasts?

I believe mine is the right answer, but maybe I am missing something

 

[David Harper CFA FRM]

I agree @joacogimeno that yours implements @cdbsmith 's alternative approach, but I don't think that is how Bodie defines the timing ability score; i.e., I think P(1) is the number of correct bull forecasts divided by total (realized) bull markets (not total predicted bull markets). The reason is that he says (emphasis mine), "An analyst who always bets on a bear market will mispredict all bull markets (P1 = 0), will correctly "predict" all bear markets (P2 = 1) and will end up with timing ability of P = P1 + P2 - 1 = 0."

If you imagine that all 14 forecasts are for bear market, then dividing by actual bull/bear markets is robust to the conclusion; ie, the answer is always 1.0. (Note he does imply that, if you predict all bear markets, the score will be zero regardless of the actual pattern ... on reflection, this makes sense to me )

But the alternative (dividing by number of predictions) is variant to outcomes:

• P(1) = 0/0 = undefined; i.e., zero bull predictions
• P(2) = number of bears/10 = 0 to 1.0