Efficient Frontier Portfolio Optimization


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:

imageSeveral 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:

image

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:

image

image

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)


AI Classification Portfolio Optimization

In the benchmark portfolio, no loan selection or filtering was used to improve performance.  This portfolio uses a random forest 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: 

image

Key Observations:

  • No G loans were invested
  • Using the classification 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:

image

image

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%


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 a classification 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.

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.

About the Author

sociallenderMariried with two beautiful daughters. Enjoy artificial intelligence, investing and Jiu-Jitsu. Life is good - Godspeed!View all posts by sociallender →

Leave a Reply