Monday, March 11, 2013

Efficient Frontier Portfolio Optimization

 

Table of Contents



Overview

The notion of diversification involves the age-old “don’t put all your eggs in one basket”.  Obviously, increasing the number of loans in your portfolio lowers risk as it minimizes the impact of defaults.  However, does diversifying the class (grade) of loans in your portfolio improve return while reducing risk?

Back in 1952, Harry Markowitz won the Nobel prize in economics based on his work with the efficient frontier (cornerstone of modern portfolio theory).  The goal is to optimize a portfolio of assets to achieve the highest expected return for a given level of risk or the lowest risk for a given level of expected return.  It is one of the most important and influential economic theories involving investment and finance.

The efficient frontier requires several data metrics including average return, standard deviation and correlation.  The following assumptions/tasks are used to derive these metrics based on historical loan data:

  • Only loans which have had enough time to mature were used to avoid issues related to artificially increased charged off rates for recent loans.  Generally, there is an higher rate of charged off non-mature loans because good loans have not been given time to mature.  In addition, no 60 month loans can be included as none were issued more than 5 years ago.
  • Returns are calculated at issue date.  In other words, the period/length of the loan in regards to return is considered instant.
  • All historical loans are categorized by month and grade.  Therefore, for each month, the average return for each loan grade is calculated.
  • Optimization is applied to portfolio loan grades where enough historical data is available to provide statistical significance.
  • Lending club commission fees were not used in the analysis

 

Benchmark Portfolio

The following table shows an “all-in” hypothetical strategy of investing in every loan issued up to Jan 2010.  In other words, this portfolio invests the same amount in every possible loan up to Jan 2010.  The following table represents the average return for each month by loan grade:

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Several key observations:

  • All loan grades provide positive average returns across all periods.  Minimum 4.15% (grade G) and Maximum 8.36% (Grade A).
  • Grade A and F loans yield average return over 8%, but A loans have significantly less risk (standard deviation 2.49% versus 16.39% respectively)
  • Only 3 negative average return months across all periods.
  • As expected, risk (Std Dev) increases from grade A to G.

Using this information, we can build an equally weighted (roughly 15% of capital in each loan grade per period) benchmark portfolio.  Remember this portfolio does not include any filtering/screening as it will be used as a benchmark.  It indiscriminately invests all available capital equally among each loan grade:

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Key Observations:

  • The average return is 6.88% with risk/stdev of 12.10%
  • Probability of achieving 5% return is roughly 56%
  • Using risk free rate of .36%, this benchmark portfolio significantly outperforms

Benchmark Portfolio Optimization

Now that we have a benchmark portfolio, lets see if modern portfolio theory using the efficient frontier improves its return and lowers risk.  Based on the average return for each period and standard deviation, we can generate a correlation matrix and optimize the portfolio:

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Key Observations:

  • Improved portfolio average return from 6.88% to 7.63%
  • Significantly reduced overall portfolio risk from 12.10% to 2.63%
  • Increased probability of achieving 5% return from 56.18% to 84.28%
  • Highest weighted loan grades are A and B (47% and 17% respectively)



Aggressive Portfolio Optimization

In the benchmark portfolio, no loan selection or filtering was used to improve performance.  This portfolio uses the aggressive model to invest only in notes that are classified as good loans.  The following table shows the average return per month if invested in every opportunity: 

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Key Observations:

  • No G loans were invested
  • Using the aggressive model to filter loans improved all average returns except grade F (could be the result of infrequency)
  • Risk (stdev) was reduced for grade A,B,C and E
  • Only one month of negative average return

Note that grade E loans performed very well but were relatively infrequent.  To avoid skewed results, we omit grade E-G in the portfolio optimization:

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Key Observations:

  • Improved average return from 6.88% (benchmark) to 9.18%
  • Significantly reduced risk from 12.10% (benchmark) to 1.70%
  • Increased probability of achieving 5% from 56.18% (benchmark) to 99.46%
  • Highest weighted loan grades are A at 71%

 

Conservative Portfolio Optimization

The conservative portfolio provides relatively low risk with increased yield by applying more cost to misclassified loans.  The following table shows the average return per month if invested in every opportunity:

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Key Observations:

  • No G - F loans were invested
  • Marginal difference in average returns compared to aggressive portfolio.  However, risk increased significantly for both B and C loans. 
  • Risk (stdev) was reduced for grade A,B,C and E
  • Only one month of negative average return

To avoid skewed results, we omit grade D-G in the portfolio optimization:

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Key Observations:

  • Improved average return from 6.88% (benchmark) to 8.64%
  • Significantly reduced risk from 12.10% (benchmark) to 2.39%
  • Increased probability of achieving 5% from 56.18% (benchmark) to 93.68%
  • Highest weighted loan grades are A at 98%
  • Reduction in overall performance compared to aggressive model

 

Risk Adverse Portfolio Optimization

The risk adverse portfolio provides minimum risk by increasing the cost of misclassified loans. The following table shows the average return per month if invested in every opportunity:

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Key Observations:

  • No D - F loans were invested (except 1 month for D)
  • Significant improvement in average returns compared to previous portfolios for grades A and B
  • Risk (stdev) similar for A and B to aggressive portfolio
  • No negative month returns for A and B loans only

To avoid skewed results, we omit grade C-G in the portfolio optimization:

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Key Observations:

  • Improved average return from 6.88% (benchmark) to 9.9%
  • Significantly reduced risk from 12.10% (benchmark) to 2.81%
  • Increased probability of achieving 5% from 56.18% (benchmark) to 95.99%
  • Highest weighted loan grades are A at 84%
  • Marginal overall improvement in average return compared to aggressive portfolio



Combined Portfolio Optimization

If we combine the portfolios (aggressive, conservative, risk adverse and all loans), we can include D-F loans and choose the most favorable loans in each grade.  The combined portfolio consists of:

  • Grade A and B loans from risk adverse model
  • Grade C loans from aggressive model
  • Grade D and E from all loans classified as fully paid

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Key Observations:

  • D and E loans on average do not provide significant improvement in return
  • F loans are infrequent.  As a result, difficult to model statistically

To avoid skewed results, we omit grade F in the portfolio optimization:

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Key Observations:

  • Improved average return from 6.88% (benchmark) to 9.76%
  • Significantly reduced risk from 12.10% (benchmark) to 2.08%
  • Increased probability of achieving 5% from 56.18% (benchmark) to 98.51%
  • Highest weighted loan grades are A at 45%

 

Editor’s Picks Portfolio

Editor’s picks portfolio selects loans from each model that meet a minimum threshold:

  • A loans from risk adverse, expected return greater than 7%
  • B loans from risk adverse, expected return greater than 8%
  • C loans from aggressive, expected return greater than 9%
  • D loans from aggressive, expected return greater than 11%
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Key Observations:

  • B,C and D loans provide excellent average returns
  • D loans have significant risk

Unfortunately, there are not enough A,B and D loans to model this portfolio. 

 

Conclusion

Here a few of my own personal opinions:

It’s hard not to make a positive return if diversified in enough loans.  Lending club boasts that 95% of investors earn between 6-18%, and 100% of investors with 800 or more notes have experienced positive returns.  Using portfolio optimization, astute investors should be able to easily achieve this claim.  However, the average return of the equally weighted benchmark portfolio across all loans is roughly 6%.  With 12% risk, it’s possible to lose money.

Optimizing a portfolio using the efficient frontier improves portfolio return and reduces risk without requiring loan filtering.  Using modern portfolio theory improved average return from 6.88% to 7.63% and reduced risk from 12.10% to 2.63%.  Optimizing your portfolio using the efficient frontier statistically removes the possibility of negative returns!

Use of statistical filtering significantly improves return and reduces risk.  For example, using the aggressive model and weighting your portfolio appropriately (see above), the following improvements were made:

  • Improved average return from 6.88% (benchmark) to 9.18%
  • Significantly reduced risk from 12.10% (benchmark) to 1.70%
  • Increased probability of achieving 5% from 56.18% (benchmark) to 99.46%

In other words, there is almost 100% chance you will reach a 5% target, with low risk(volatility).  This is a significant achievement in today’s market.

The editor’s pick portfolio does show some statistical significance that using a minimum expected return threshold improves performance.  However, there is not enough historical evidence to support this claim in loan grades other than C.

Based on popular belief, I am surprised that grades E-G did not perform as well as I would have expected.  Not only did they show marginal if any improvement in average return, but significantly higher risk (in optimized benchmark and all loans model) .  As a result, the efficient frontier weighted these loans in the lower percentile.  This could be the result of sub-optimal filtering (maybe there are better filters out there for high risk loans) or just the nature of these types of loans.  On the other hand, grades A-C filtered using the aggressive portfolio provides very good results.  Obviously, if you are very good at selecting these types of loans, your average return should improve as well as reduction of risk.  I anticipate in a few more years when more historical data is available, the system’s statistical methods to filter E-G loans will improve.

It is important to note that the efficient frontier does not seek to provide the maximum level of return regardless of risk.  Rather, the maximum level of return for a given level of risk.  This is reflected in the Sharpe ratio which measures risk adjusted performance (volatility).  For the majority of investors, steady growing revenue is generally preferable versus higher returns with significant volatility.

If you have been using this site for a while, you may have noticed that minority filters have been removed.  Unfortunately, they proved to be ineffective at providing an additional layer of confidence in loan selection.  They did not hurt, but provided no real significant improvement.  I made the decision to remove this feature as it required significant CPU power. 

Based on the evidence I have seen so far, I am leaning toward a portfolio of heavy C, B, A and D loans (in that order) which meet a minimum expected return threshold.  I may consider investing in loans with a high interest rate (above 14% for example) provided its classified as a good loan.  This obviously would increase risk (along with return hopefully) but may be worthwhile based on other investors feedback.

 

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