Asset Allocation - choosing the optimal portfolio

CFA Level III Portfolio Management
#1

Emma Young, a 47-year-old single mother of two daughters, ages 7 and 10, recently sold a business for $5.5 million net of taxes and put the proceeds into a money market account. Her other assets include a tax-deferred retirement account worth $3.0 million, a $500,000 after-tax account designated for her daughters’ education, a $400,000 after-tax account for unexpected needs, and her home, which she owns outright.

Her living expenses are fully covered by her job. Young wants to retire in 15 years and to fund her retirement from existing assets. An orphan at eight who experienced childhood financial hardships, she places a high priority on retirement security and wants to avoid losing money in any of her three accounts.

A broker proposes to Young three portfolios, shown in Exhibit 1. The broker also provides Young with asset class estimated returns and portfolio standard deviations in Exhibit 2 and Exhibit 3, respectively. The broker notes that there is a $500,000 minimum investment requirement for alternative assets. Finally, because the funds in the money market account are readily investible, the broker suggests using that account only for this initial investment round.

Exhibit 1

Proposed Portfolios

Asset Class Portfolio 1 Portfolio 2 Portfolio 3
Municipal Bonds 5% 35% 30%
Small-Cap Equities 50% 10% 35%
Large-Cap Equities 35% 50% 35%
Private Equity 10% 5% 0%
Total 100% 100% 100%

Exhibit 2

Asset Class Pre-Tax Returns

Asset Class Pre-Tax Return
Municipal Bonds 3%
Small-Cap Equities 12%
Large-Cap Equities 10%
Private Equity 25%

Exhibit 3

Portfolio Standard Deviations

Proposed Portfolio Post-Tax Standard Deviation
Portfolio 1 28.2%
Portfolio 2 16.3%
Portfolio 3 15.5%

Young wants to earn at least 6.0% after tax per year, without taking on additional incremental risk. Young’s capital gains and overall tax rate is 25%.

According to CFAI, the right answer is portfolio 3. Portfolio 1, 2 and 3 have after-tax returns of 9.15%, 6.64% and 6.68% respectively. When you analyze risk-adjusted return using Roy Safety first ratio (Er-MAR/st deviation): for Portfolio 1, 2 and 3 you get 11%, 4% and 4% respectively which makes portfolio 1 the most efficient to me. Further, Portfolio 1 meets the minimum alternative investment (PE allocation of 10%). Can someone explain why portfolio 3 is still the right answer? Thanks!

#2

Portfolio 3 has the greatest sharp ratio, more importantly the clients return requirement can be met (6% return) with the lowest amount of risk (standard deviation of returns) which is a high priority for this risk averse client.

#3

Should also add that the 500k minimum is simply a minimum investment to get exposure to the PE asset class. This helps you rule out portfolio 2 because 5% of 5.5m doesn’t meet the .5m minimum investment.
The client doesn’t explicitly state they would like exposure to PE.

#4

Thank you! How are you calculating a Sharpe without a given risk free rate? I thought the RSF ratio would be more appropriate here given a minimum threshold. How should we know which ratio is applicable when?

#5

The ratios are essentially the same only the RSF ratio replaces the risk free rate with the minimum return requirement. You should review your RSF calculations as the answers don’t appear accurate.

Key point to remember here is the risk averse natural of the client

#6

So the expected after-tax return #s are accurate as verified by the CFAI answers itself.

With the given standard deviations and MAR of 6%, I would assume the RSFs for pf 1,2 and 3 would be respectively : (9.15-6)/28.2= 11%, (6.64-6)/16.3=4% and (6.68-6)/15.5=4%…Would you plz mind pointing out any flaws in my RSF formulae? Thanks

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#7

I stand corrected, the issue here then is the use of the RSF ration rather than the sharp ratio. I would always default to the sharp Vs the RSF to understand the return per unit of risk when figuring out which portfolio is more efficient.
The key point here is the clients risk aversion so if you can generate the required return by taking less risk it’s typically the most appropriate option even if that option isn’t the most efficient in terms of risk adjusted returns.
Not to over analyse the question but when you focus on efficiency e.g. ratios, you need be be aware of their flaws. The obvious one here is that PE exposure - much like property, can rely on appraisal pricing which smooths returns and makes them appear very efficient when in reality, there just isn’t a frequent mark price to accurately reflect the true deviation of returns.

#8

Ok so just got a question wrong in the CFA Qbank that has cleared up when you would use the RSF ratio rather than the sharp. If the question ask which portfolio has the “highest probability” of enabling a client to meet their return objective, use the RSF ratio.
Sharp ratio is all about efficiency of returns on a risk adjusted basis

#9

Ok very helpful and makes sense, thanks! I should have included that this question was framed as:

Q. Determine which proposed portfolio most closely meets Young’s desired objectives.

One last question on this sorry! What risk free rate exactly are we using to calculate to calculate the SR? Probably less relevant as you mentioned in this case, there are other factors into play including the PE issue, but just curious.

-Maisha

#10

The sharp ratio tells you what level of return is per unit of risk taken. With this in mind if a risk free rate isn’t provided assuming zero or that the returns provided are above a risk free rate is fine as long as the approach is consistent across each of the portfolios you are relatively assessing.

You could answer this question by simply calculating the returns, discovering that they all meet the return requirement of 6% and then simply look for the portfolio that has the lowest standard deviation of returns. The more I look at this question the more I realise calculating a sharp or a RSF ratio isn’t a necessary step

#11

Maisha did you asked to CFAI if there is any error? Do you have the complete answer from CFAI? Because it’s so confusing to me:

  1. I agree with Tez4715 that SR should be a possible way, but it’s so strange that they provide the minimum return (6%) and not the risk free…it is not aligned to other questions format and really misleading
  2. If the minimum 500k investment in alternative asset is a requirement, only PF1 respect this condition

The only way to be PF3 (and in this I agree with the last reply of Tex4715) is that “Young wants to earn at least 6.0% after tax per year, without taking on additional incremental risk”
In this case the point could be to select the PF with lower volatility, given that it’s after tax return is at least 6% (make sense??)…but it’s still not clear the 500k of alternative investment requirement.

Bye

Ste

#12

Hello there, yes I agree in that I find the question very misleading given no rf rate and only MAR.

I haven’t reached out to CFAI, not sure exactly who/which department to contact and how?

Here’s the below answer from CFAI which makes sense, but again not completely given how the question is framed and lack of rf rate.

Determine which proposed portfolio most closely meets Young’s desired objectives. (Select one.)

Q. Justify your response to the previous question.

Solution

Portfolio 3 comes closest to meeting Young’s desire to earn at least 6% after tax per year without taking on additional incremental risk. Portfolio 3 offers a lower standard deviation than Portfolio 2, as summarized in Exhibit 3, while producing approximately the same return. Portfolio 1 achieves the highest returns but at a much greater level of volatility than Portfolio 3, not satisfying Young’s risk criterion.
Given the $500,000 minimum investment requirement for alternative assets, at Young’s total portfolio size of $5.5 million, the suggested 5% allocation to private equity in Portfolio 2 results in only a $275,000 exposure, insufficient to invest in private equity. Thus, Portfolio 2, as presented, is not viable, whereas Portfolio 1, with a private equity investment of $550,000, meets the minimum requirement for alternative investments. This minimum investment requirement is not an issue for Portfolio 3 because it has no private equity component.

Asset Class Portfolio 3 Pre-Tax Return Post-Tax Return Resulting Return
Municipal Bonds 30% 3% 3.00% 0.90%
Small-Cap Equities 35% 12% 9.00% 3.15%
Large-Cap Equities 35% 10% 7.50% 2.63%
Private Equity 0% 25% 18.75% 0.00%
Total 100% 6.68%
Asset Class Portfolio 1 Pre-Tax Return Post-Tax Return Resulting Return
Municipal Bonds 5% 3% 3.00% 0.15%
Small-Cap Equities 50% 12% 9.00% 4.50%
Large-Cap Equities 35% 10% 7.50% 2.63%
Private Equity 10% 25% 18.75% 1.88%
Total 100% 9.15%
Asset Class Portfolio 2 Pre-Tax Return Post-Tax Return Resulting Return
Municipal Bonds 35% 3% 3.00% 1.05%
Small-Cap Equities 10% 12% 9.00% 0.90%
Large-Cap Equities 50% 10% 7.50% 3.75%
Private Equity 5% 25% 18.75% 0.94%
Total 100% 6.64%
#13

From the answer I understand the the solution suggested by Tex4715 is the proper one: no need to calculate the RSF, but select the PF with lower volatility with a minimum return higher than 6%. I don’t understand the point about alternative assets, it’s like to say that it is minimum 500k if there is already some alternative asset

#14

See the above comment, you don’t need to worry about PE exposure here

#15

@Tez4715

Continuing from the sharpe ratio topic, below is a question from the equity section which I find pretty confusing. In the below case for the best “risk-efficient” portfolio, we are not supposed to choose the one with the highest sharpe and lowest vol…But not entirely sure when/how to decide which measure is important when. In this case we are supposed to look at active risk and active share and ignore the fact that “March” doesn’t have the best sharpe.

Lisette Langham Case Scenario

Lisette Langham is an independent consultant specializing in analysis of active equity portfolio management, and in her work she often uses such accepted concepts as alternative beta, Active Share, and active risk. A client, Bob Shaw, asks her to help evaluate various funds he owns that are managed by the Master Fund Company (MFC). Langham describes how she uses rewarded factor analysis, regardless of whether a manager uses factor exposure explicitly. She shows Shaw her analysis of the MFC Value Fund compared with its benchmark (Exhibit 1).

Exhibit 1

Rewarded Factor Results

Factor Sources of Performance over 15 years Market Russell 1000 Value (Benchmark) MFC Value Fund
Market 0.71% 0.59% 0.50%
Size 0.0% –0.04% 0.02%
Value 0.0% 0.08% 0.11%
Momentum 0.0% 0.08% 0.05%
Alpha (non-factor related) 0.0% –0.05% –0.05%
Total monthly performance 0.71% 0.66% 0.63%

On viewing Exhibit 1, Shaw makes the following comments about the MFC Value Fund:

  • The small-cap tilt helped.
  • Value funds were out of favor, as shown by the Value factor results.
  • Of course, the MFC Value Fund must have a lower alpha because its performance was 0.03 percentage point worse than its benchmark.

Shaw has particular interest in MFC’s popular Soar Fund (Soar), which relies on returns from factor exposures. The description of the fund states that it emphasizes security-specific factors, maintains low security concentration to keep idiosyncratic risk down, and embraces quality and value styles. Soar occasionally considers the economic and geopolitical environment, especially during unusual economic conditions. Langham tells Shaw how she classifies Soar’s portfolio construction approach.

Noting that MFC has two managers who use the same index as their benchmark, Shaw observes that Fund A and Fund B have similar Active Share and a similar number of positions, but Fund A’s realized active risk of 7% is almost three times greater than that of Fund B. Shaw makes the following comments:

  • I think Fund B makes a lot of sector bets.
  • Fund A likely has higher fees than Fund B
  • Fund A should have a greater dispersion of returns about the benchmark.

Shaw next asks Langham to show how risk targets and constraints might differ between fund managers depending on their respective skills. Langham has Shaw consider three fund managers, each of whom use the MSCI World Index benchmark. For each fund, risk targets have been assigned that allow the portfolio managers some flexibility to exercise their perceived skillsets. Skills include stock picking, factor exposure, and sector rotation. Based on only the data shown in Exhibit 2, Langham identifies the skill applied by each manager.

Exhibit 2

Risk Targets and Constraints

Manager constraints Fund X Fund Y Fund Z
Target active risk 8% 7% 4%
Max . sector deviations 1% 15% 10%
Max . risk contribution, single security 4% 2% 1%

Another of Langham’s clients, Marianne Quint, sits on the investment committee of the Amity Island Endowment. The $2 billion equity portion of the Amity fund is invested using a global equity index approach. Quint has been charged with identifying an active equity fund to replace 20% of the indexed portfolio. Three candidate funds with similar performance histories, benchmarks, and fees have been identified. Based on the characteristics shown in Exhibit 3, Quint asks Langham to recommend the fund that has demonstrated the best risk-efficient delivery of results.

Exhibit 3

Characteristics of Candidates for Amity Equity Portfolio

Fund Name Blue Ash March
Sharpe ratio 1.11 0.90 0.92
Annualized active risk 5.5% 6.0% 3.2%
Active Share 0.41 0.48 0.75
Number of securities 340 290 140
Annualized portfolio volatility 11.5% 14.7% 14.9%
Covariance with Amity Fund Low High Low

Langham also identifies the fund that could minimize the active risk of the total $2 billion Amity equity portfolio after replacement is complete.

Q. The fund in Exhibit 3 that is most consistent with Quint’s requirements is:

  1. Ash.
  2. Blue.
  3. March.

Solution

C is correct. The March Fund is the fund that is most consistent with Quint’s requirements for the best risk-efficient delivery of results. It delivers the lowest active risk (3.2%) using far fewer securities (140), indicating an efficient approach. The higher Active Share (0.75) for the similar level of fees also supports this decision.

#16

Hi Maikhan,

I think the issue here is probably the poorly worded question. The endowments equity exposure comes from a passive (index) approach and 20% of this passive exposure is being replaced with an “active” equity approach. This is why Sharp ratio seems like the logical first metric to look at.
The Ash portfolio can be ruled out because of the high covariance with the existing fund, risk adjusted returns can be improved with diversification which leaves Blue and March.
When answering this question I actually went for Blue because of the higher sharp and the low tracking error (active risk) of March is not appealing for an active strategy. Knowing I got the answer wrong, I can rationalise with knowing that March actually has a higher active share which rules out concerns of a closet tracker, the number of securities is significantly lower than Blue so I guess this is more “risk-efficient” because both portfolios will probably not have a concentrated portfolio (top 10 weight) but March achieves this with significantly less stocks.

Can’t get them all right and I hope on exam day the questions will be better worded than this :crossed_fingers:
Maybe someone else can provide you with a better answer here.

#17

Yep hopefully every question is not a trick question on the exam, but thanks for the explanation!

-Maisha

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#18

I don’t know if I’m confused but understand that the process should be:

  1. Select the PF with lower unexeplained risk (not given), then
  2. Select the PF with lower active risk (March) e absolute risk (Blue)
  3. If the PFs have similar active e absolute risk, alpha skills and fees (this is the case) then select the PF with higher Active share to leverage manager skills (March).
  4. If 2 PF can invest only in the same benchmark, the PF with fewer securities have higher active share
#19

Starting with active risk here is probably a good approach, thanks!