cfa 2019 AM mock question 42

CFA Level III
#1

hi all

for this question, you have three funds, one of them has the lowest tracking error but it has low correlation with the existing portfolio.

the objective is to add a portfolio to the existing one that reduces tracking error.

for me, the best way to reduce the tracking error is to pick the portfolio that has the lowest tracking error even if it is not highly correlated with the existing fund as it will drive the whole closer to the benchmark

CFA answer suggest to look for the fund that is more highly correlated to your existing portfolio,

any one know where is the flaw in my rationale?

thanks

#2

Liability requires higher correlation

#3

To me this question as a whole is quite unclear. First of all, what are the benchmarks the active risk is measured against? For the three funds it is merely stated that those are “similar” benchmarks. What is the benchmark of the overall portfolio? Is it also similar to the benchmarks of the funds? (I assume its not). Keeping this in mind I think a solution could be:

The original fund is an index portfolio, which should have low active risk in relation to its benchmark (presumably the global equity index). If you add something that is highly correlated with the initial fund it will also be highly correlated with the initial funds benchmark (active risk of initial fund is low), thus you minimize active risk of the resulting portfolio by choosing the high correlation option.

One problem remains: How can this fund (Ash) have high active risk even though it is highly correlated with the original fund and the original funds benchmark? That is only possible if Ash’s benchmark is different from the original funds benchmark.

So using a handful of assumptions you can get there, but they could have used some more explanations (at least in the answer).

#4

Hey Renewables,

So the Amity Endowment currently creates their $2B equity exposure using a Global Equity Index approach.

Here are the mental steps to take to get there:

  1. Recognize that the focus is on reducing tracking error (active risk) of the total $2B equity portion even though we’re only tasked with replacing 20% of it.
  2. Active risk is measured relative to a benchmark (We aren’t told what the benchmark is here, but it doesn’t matter)
  3. If we want to swap out 20% of current holdings with a new set of holdings and keep tracking error low, it follows that we want securities that will move with the remaining 80% of the holdings. (We don’t want a fund that zigs while everyone else zags)
  4. Selecting the fund that can minimize active risk after replacement is complete is then a simple process of looking at the one metric that tells us how a portfolio of securities moves in relation to another: covariance.
  5. Ash is the only fund with high covariance with the rest of Amity’s Fund. They are zigging while Amity is zigging.

Footnotes

  • Annualized active risk is thrown in there to throw you off. It is only relevant when comparing different funds to the same benchmark- no mention is made of the benchmark used for Amity vs the 3 different benchmarks used for Blue, Ash, & March (Sounds like a set of Kim Kardashian kids)
  • Sharpe Ratio & Annualized Portfolio volatility is also in there to throw you off. They are measures of total risk and should immediately be eliminated since the question is asking for active risk (which is measured relative to a benchmark)

And if none of that made sense, here’s an example scenario where a fund with low active risk and low covariance could add active risk to Amity’s Fund. Let’s use the March Fund with 3.2% annualized active risk

  • Amity is described as a Global Equity index approach. Let’s for arguments’ sake say that the entire Amity Global Equity Fund has exposure to Global Large Cap names in primarily developed markets (90% of index cap).
  • Also, for argument’s sake, let’s say that Ash’s strategy is Global Large Cap with the same tilt towards developed markets (90% of index cap).
  • However, let’s say that March’s strategy, while also a Global Large Cap Equity, has a slightly smaller tilt towards developed markets (only 80% of index cap in developed markets)
  • March’s 3.2% Active risk, relative to its Global Large Cap Equity Strategy is admirable. Clearly, the benchmark they use has similar exposure to developed / emerging markets (80/20)
  • If you plug in the March Fund to the Amity Fund, the overall tracking risk could increase, since the overall Fund exposure has moved from 2% (20% * 10%) exposure to EM to 4% (20% * 20%) exposure to EM.
  • The Low covariance of March’s returns with the Amity returns is reflected in this example by the difference in geographical exposure.
  • In contrast, the Ash Fund’s same 90/10 DM / EM split plugs in quite nicely with Amity’s overall strategy and, regardless of Ash’s active risk relative to Ash’s benchmark, would better move in the same direction with Amity’s existing holdings, reducing Amity’s active risk relative to Amity’s Benchmark. (sorry for the wordiness, trying to avoid misplaced modifiers)

Hope this helps…best of luck!

1 Like
#5

Many thanks brickbreaker!

it makes sense with the zigs and the zags :slight_smile: