Portfolio Optimization Paradox: Weaker Components May Lead To Higher Portfolio Performance

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Includes: IVV, IWM, MDY, SPY, TLT, VB, VO
by: Toma Hentea

Summary

Two four-ETF portfolios, comprised of TLT plus a set of three equity ETFs each, are compared at different time frame intervals.

The assets of one portfolio (SPY, MDY, IWM) underperform the corresponding assets of the second portfolio (IVV, VO, VB) at all time frames, regardless of the type of market.

As expected, the portfolio with stronger assets performs better than the one with weaker assets when the portfolios are created with fixed weights in a buy-and-hold mode.

Paradox: The portfolio with weaker assets performs better than the one with stronger assets when the portfolios are managed by adaptive asset allocation.

Recently a friend from the Chicago South Suburban Investment Club brought to my attention an issue with our selection of ETFs for our Adaptive Allocation Portfolio that was the subject of my earlier article. In an article in Barron's March 2, 2015 issue, Chris Dietrich described an anomaly with U.S. Small-Cap ETFs, showing that there is a significant performance variation of their performance. And, as usually happens, it turned out that our choice, the iShares Russell 2000 ETF (NYSEARCA:IWM) was the underperformer.

I took it upon myself to investigate this matter, so I analyze all the assets in our portfolio and found out that on an individual basis, one-on-one, our mid-cap and large-cap ETFs were also underperforming relative to their counterparts. It was just natural to decide to look further and determine the effect of these presumably bad choices on the performance of our portfolio.

In this article I compare the performance of two portfolios built with a long-term bond ETF and two subsets of equity ETFs.

Our portfolio has the following four ETFs as components:

  • iShares 20+ Year Treasury ETF (NYSEARCA:TLT)
  • SPDR S&P500 ETF (NYSEARCA:SPY)
  • SPDR S&P400 ETF (NYSEARCA:MDY)
  • iShares Russell 2000 (IWM)

The competing portfolio is comprised of TLT plus the following three ETFs:

  • iShares Core S&P 500 (NYSEARCA:IVV)
  • Vanguard Mid-Cap ETF (NYSEARCA:VO)
  • Vanguard Small-Cap ETF (NYSEARCA:VB)

The above two portfolios were simulated with historical data, downloaded from Yahoo Finance.

We use daily price data from March 2005 to March 2015, adjusted for splits and dividends. We considered the following three time periods: three-, five- and ten-year intervals.

In table 1 we show the performance of the individual assets over the three time intervals.

Table 1. Performance of individual ETFs over 3-, 5- and 10-year period.

3Y CAGR%

3Y VOL%

5Y CAGR%

5Y VOL%

10YCAGR%

10Y VOL%

SPY

17.80

11.93

16.05

15.80

8.00

20.37

IVV

17.91

11.94

16.11

15.85

8.03

20.02

MDY

16.58

14.00

16.66

19.02

9.93

23.64

VO

18.26

13.35

17.66

18.40

9.98

22.91

IWM

15.83

15.80

15.90

21.74

8.54

25.86

VB

17.39

14.56

17.31

20.52

9.89

24.75

TLT

6.21

12.94

10.79

15.34

7.64

14.36

To use as a reference for comparison, we simulated the performance of the two portfolios with fixed allocation, 25% in each asset, in a buy-and-hold mode without rebalancing. The results are showed in the table 2.

Table 2. Performance of portfolios with equally weighted fixed allocations

3Y CAGR%

3Y VOL%

5Y CAGR%

5Y VOL%

10Y CAGR%

10Y VOL%

SPY+MDY+IWM+TLT

14.29

9.53

14.95

12.09

8.56

14.63

IVV+VO+VB+TLT

15.16

9.15

15.60

11.72

8.93

14.21

We also computed the performance of the two portfolios with equal target weights using rebalancing when the deviation of any asset deviates by more than 10%. The results are given in table 3.

Table 3. Performance of portfolios with target allocations rebalanced at 10% deviation

3Y CAGR%

3Y VOL%

5Y CAGR%

5Y VOL%

10Y CAGR%

10Y VOL%

SPY+MDY+IWM+TLT

14.50

9.13

15.76

12.17

9.35

15.84

IVV+VO+VB+TLT

15.43

8.81

16.33

11.79

9.66

15.38

A few observations can be made by analyzing the results in tables 2 and 3:

  1. The portfolio (IVV, VO, VB, TLT) achieved between 0.31% and 0.93% higher CAGR than the portfolio with (SPY, MDY, IWM, TLT). That is consistent with the contribution of the components.
  2. The volatilities of both portfolios are substantially lower than the volatilities of the components.
  3. Rebalancing improves the performance of both portfolios compared to the fixed buy-and-hold strategy.

As described in a couple of our published articles, we use an adaptive allocation strategy to manage our investments. The portfolios are invested dynamically among the four funds based on a variance-return optimization algorithm. The allocation is rebalanced at fixed one-month intervals.

We decided to simulate the adaptive allocation strategy for the two portfolios to determine if we should switch to the stronger set of ETFs. We considered three levels of volatility targets: low, medium and high, and we simulated the portfolios over 3-, 5- and 10-year time intervals. The results are presented in tables 4, 5 and 6.

Table 4. Performance of portfolios with adaptive allocations - LOW volatility

3Y CAGR%

3Y VOL%

5Y CAGR%

5Y VOL%

10Y CAGR%

10Y VOL%

SPY+MDY+IWM+TLT

12.56

7.95

16.00

8.36

10.12

9.58

IVV+VO+VB+TLT

11.74

7.99

15.49

8.39

9.94

9.51

Table 5. Performance of portfolios with adaptive allocations - MEDIUM volatility

3Y CAGR%

3Y VOL%

5Y CAGR%

5Y VOL%

10Y CAGR%

10Y VOL%

SPY+MDY+IWM+TLT

12.65

9.73

19.27

10.61

12.65

11.27

IVV+VO+VB+TLT

11.34

9.72

18.61

10.56

12.16

12.16

Table 6. Performance of portfolios with adaptive allocations - HIGH volatility

3Y CAGR%

3Y VOL%

5Y CAGR%

5Y VOL%

10Y CAGR%

10Y VOL%

SPY+MDY+IWM+TLT

13.90

11.25

21.86

12.54

14.21

12.97

IVV+VO+VB+TLT

13.09

11.25

21.35

12.50

14.20

12.84

By analyzing the results in tables 4, 5 and 6 we are making the following broad observations:

  1. The results are consistent with the trade-off between returns and volatilities. By targeting a higher volatility we can achieve higher returns but that comes with higher volatility of the returns.
  2. In all three tables meaning for all levels of volatility targets, as well as for all time intervals, the portfolio with {SPY, MDY, IWM, TLT} produces higher returns than the portfolio with {IVV, VO, VB, TLT}. In most cases, but not all, the former portfolio has also lower volatility of the returns.

We do not have any sound explanation of the observed phenomenon.

Conclusion

As stated above, we do not have any sound explanation of the observed phenomenon. By construction, the two portfolios are expected to perform almost identically, and so should do all their components. The reality is, they do not. IWM and MDY clearly underperform VB and VO. In fact, the author of the Barron's article recommends investing in VB as opposed to IWM. The same recommendation holds for portfolios with fixed allocations and periodic rebalancing.

On the other hand, we showed that if the portfolios are optimized for maximum returns at fixed volatilities, it is not a given that the portfolio with stronger components outperforms. Obviously, there are other factors that influence the performance. The only recommendation we can make is that one should always consider the possibility that a portfolio with weaker components could outperforms, and as such, one should not base his selection of portfolios assets solely on their individual performance.

Disclosure: The author is long SPY, IWM, TLT.

The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.