1. Portfolio evaluation
Chapter 15

2. Active vs passive management
The debate over active vs. passive management has raged on for many years and will continue for many, many more.
It was only a goal of this text to provide you with a sufficient amount of information so that you are comfortable making the “active vs. passive” decision for yourself.

3. Passively-managed strategy
The only decision that the passive investor needs to make is the asset allocation decision.
Since individual security analysis is not required; making investment choices is significantly less time consuming than actively-managing accounts.
However, some effort is still required in order to maintain the proper allocation of assets.

4. Re-allocation (passive)
The passive investor must still decide on the proper asset allocation, and the allocation decision can change over time.
Investor in his/her 20s?
Investor in his/her 60s?

5. Re-balancing (passive)
An investor’s initial allocation of assets will change over time based simply on the performance of the accounts.
Some asset classes will outperform other asset classes, causing an imbalance of the desired asset allocation.
In order to maintain the proper asset allocation, it is important for investors to regularly rebalance their portfolio by periodically selling those asset classes that have become overrepresented in the portfolio and buying those asset classes that have not kept pace.

6. Actively-managed portfolio
In their attempts to beat the market, investors who choose an actively-managed strategy may:
Engage in active asset allocation – selling asset classes that the investor believes will under-perform and buying those asset classes that the investor believes will out-perform the overall market.
Engage in industry/sector rotation – selling industries and sectors that the investor believes to be overvalued and buying those industries/sectors believed to be undervalued.
Engage in security selection – the buying and selling of individual securities within a portfolio based on the favorability of the security’s outlook.

7. Measuring performance with cash inflows/outflows
Measuring the performance of portfolios in which you are regularly contributing (or withdrawing) funds can be a little tricky.
In fact, there are basically two methods for calculating the returns of a portfolio that are both technically correct – but can provide different results.
Internal rate of return (IRR)
Time-weighted return (TWR)

8. IRR
The IRR finds the return that yields the portfolio’s ending value based on the amount of time that each cash flow has been available for investment.
For example: What is the IRR of your IRA from the previous example? Recall that the IRA was worth $25,000 on 1/1/ You contributed $5,000 to the IRA on 10/1/ And the IRA was worth $31,000 on 12/31/2015.
To find the IRR, you would use the following formula:
($25,000(1+IRR)3/4 + $5,000)(1+IRR)1/4 = $31,000
In this example, the additional $5,000 cash flow was made on October 1st. Adjusting for one full year, the October 1st contribution date falls exactly three- fourths into the year. Therefore, the initial cash flow of $25,000 was available for investment for ¾ of the year; whereas the additional $5,000 cash flow was only available for investment for ¼ of the year.
Solving by trial-and-error results in an IRR of approximately 3.81%

9. TWR
The time-weighted return (TWR) is the compound rate of growth in the portfolio.
For example: What is the time-weighted return (TWR) of your IRA from the previous example. Recall that the IRA was worth $25,000 on 1/1/ You contributed $5,000 to the IRA on 10/1/ And the IRA was worth $31,000 on 12/31/2015 and the IRA’s value on 9/30/15 was $25,150.   
To find the TWR, you begin by calculating the returns for the two sub periods:
Jan-Oct return = ($25,150 - $25,000) / $25,000 = .6%
Oct-Dec return = ($31,000 - $30,150) / $30,150 = 2.82%
Once the returns for the sub periods have been calculated, geometrically link the sub periods by multiplying (1 plus each sub period’s return) with the other(s).
Time-weighted return = (1 + Return Jan-Sept)(1 + Return Oct-Dec) – 1
Time-weighted return = ( )( ) – 1 = 3.44%

10. IRR vs TWR
As a rule of thumb, if you are actively managing your portfolio by engaging in asset allocation or sector rotation, then the IRR may be a better measure.
The IRR considers the timing of the investment decision (which is important to active asset allocators and/or sector rotators).
On the other hand, if you are simply contributing funds to the account with no specific regard for the timing of the investment – then the TWR may be a better measurement.
The TWR will not reward or punish your portfolio’s return for the timing of the cash flow.

11. Measuring performance (passive)
The passive investor’s portfolio performance would likely exactly match a benchmark’s performance, if not for the fees associated with each fund.
Therefore, the passive investor’s goal would be to find the least expensive funds available that match the desired asset class.

12. Measuring performance (active)
Active managers will compare the performance of their asset classes to a chosen index/benchmark in similar fashion to that of passive managers.
However, the raw return differences of active managers to the benchmark portfolios are likely to vary wildly.
In order to truly understand the performance of the portfolio, you must incorporate risk into the equation. This can be done with:
Sharpe ratio
Treynor ratio
Jensen’s alpha

13. Performance evaluation measures
Sharpe Ratio
Measures performance as the ratio of portfolio risk premium over portfolio return standard deviation.
Treynor Ratio
Measures investment performance as the ratio of portfolio risk premium over portfolio beta.
Jensen’s Alpha
Measures investment performance as the raw portfolio return less the return predicted by the CAPM.

14. Sharpe Ratio Sharpe ratio = Rp–Rf/ơp
The portfolio risk premium is the raw portfolio return less a risk-free return (which we know is the basic reward for bearing risk). The return standard deviation is a measure of total risk (previously discussed).
Thus, the Sharpe ratio is a reward-to-risk ratio that focuses on total risk.

15. Sharpe example
Over a recent 3-year period, the average annual return on a portfolio was 20%, and the annual return standard deviation was 25%. T-bills are at 5%. What is the Sharpe ratio for this portfolio during the 3-year period?
Sharpe = /.25 = .6
This indicates that the Sharpe ratio of portfolio excess return to total risk is .6.

16. Treynor Ratio Treynor ratio = Rp–Rf/βp
As with the Sharpe ratio, the Treynor ratio is a reward-to-risk ratio. The key difference is that the Treynor ratio looks at systematic risk only, not total risk.

17. Treynor example
Over a 3-year period, the average return on a portfolio was 20%, and the beta for the portfolio was During the same period, the average return on T-bills was 5%. What is the Treynor ratio for this portfolio?
Treynor = /1.25 = .12
This reveals that the Treynor ratio of the portfolio excess return to portfolio beta is .12.

18. Jensen’s alpha
Recall that a portfolio’s expected return can be written as:
E(Rp) = Rf + [E(RM)-Rf] X βp
To compute Jensen’s alpha, we compare the actual return, Rp, to the predicted return. The difference is the alpha, denoted by αp:
Jensen’s alpha = αp = Rp – E(Rp)
= Rp – {Rf+[E(Rm)-Rf] X βp}
This is the excess return above or below the SML, and can be interpreted as a measure of how much the portfolio “beat the market”.

19. Jensen example
Over a 3-year period, the average annual return on a portfolio was 20%, and the beta for the portfolio was T-bills were 5%, and the average return on the market portfolio was 15%. What is Jensen’s alpha during this period?
α = .20 – [.05+( )1.25] = .025
This portfolio has a higher than expected return given its level of systematic risk.

20. Comparing performance measures
Investment performance data
Portfolio performance measurement

21. Which one should you use?
It depends.
Many analysts may place more weight on the Sharpe ratio when analyzing a “held alone” portfolio in which total risk may be a more important measurement than only systematic risk.
The Treynor ratio and Jensen’s alpha may be better utilized in the analysis of portfolios that are part of a much more diversified total portfolio.

22. Using Morningstar’s Star Ratings
Companies are put into peer groups based on Morningstar style definitions
Risk adjusted fund performance is ranked and then Stars are assigned according to the following table (5 stars is the highest rating)
Morningstar assigns only one star to the bottom 10% of the funds it evaluates.
Morningstar assigns two stars to the next 22.5% of funds it evaluates.
Morningstar assigns three stars to the middle 35% of funds it evaluates.
Morningstar assigns four stars to the 22.5% of funds just below the top 10%.
Morningstar assigns five stars to the top 10%.

23. Style analysis using Morningstar style box
Checking the history of the fund’s style will provide insight into the fund’s style drift.
If the fund’s equity classification changes from year to year, then the fund suffers from style drift.
Year over year –
this fund changes its style
Year over year –
this fund remains consistent

24. Asset allocation vs. security selection
How can you determine:
If a manager is able to beat the market return?
If the manager over/under performs the market return due to:
His/her asset allocation decision
His/her ability to pick winners (security selection)

25. Compare the portfolios
First, take the weighted average return for the portfolio and the index.
Manager’s return = 11.4%
Benchmark = 11.15%
The benchmark’s return = 8.25% + 1.5% + 1.4% = 11.15%
The manager’s return = 5% + 2.2% + 4.2% = 11.40%
The manager has a superior return – but is it do to asset allocation or security selection?

26. Contribution of security selection
Had the manager simply chosen to invest in the benchmark indices, the manager would have enjoyed an increase in total returns by 30 basis points.
Bogey = 7.6

27. Contribution of asset allocation
In this example, it appears that the manager’s decision to pull money out of the lower performing large-cap stocks and reinvesting the funds in the higher performing mid-cap and small-cap stocks was instrumental in the manager’s outperformance of the index. This asset allocation decision resulted in a total return increase of 55 basis points.

28. Choosing appropriate benchmarks
Benchmarks should be unambiguous. You should be able to see exactly what the benchmark includes.
Benchmarks should be measurable. You should be able to easily find updated numbers on your benchmark.
Benchmarks should be appropriate. For instance, you shouldn’t use an international small-cap value benchmark to assess the performance of a domestic large-cap growth portfolio.
Benchmarks should be specified in advance. For instance, when you see that your performance is lower than your originally chosen benchmark, you may wish that you could switch to another benchmark (perhaps one that you are beating). While tempting, this is not acceptable. If there is reason to change benchmarks – you must specify in advance the need for the change.