Many investors are familiar with the concept of diversification. Diversification spreads risk across multiple investments, so that one or two failures can be adequately compensated by the remaining well-performing investments. This is an important strategy for maintaining a healthy portfolio.

##### Why does diversification matter?

To illustrate the usefulness of diversification, we first need to understand the nature of risk in a credit portfolio. We can think of risk as coming from two sources:

*Systematic risk*, or the risk that borrowers fail to pay back due to worsening macroeconomic conditions facing an industry or a market; and*Idiosyncratic risk*, or the risk that borrowers fail to pay back for reasons affecting only them.

Diversification helps us address the second risk: as we add more and more investments to our portfolio, the idiosyncracies of our individual investments start to cancel out, and the idiosyncratic risks go away. Our returns become more predictable. With very large portfolios spread thin over many investments -- portfolios with high “granularity” -- all we need to worry about is systematic risk, like a recession or a force majeure event. Diversification takes care of the rest.

To see how this happens, consider the chart below. We consider hypothetical portfolios with between 1 and 200 loans, make some assumptions about these loans, and run a Monte Carlo simulation of 20,000 scenarios to estimate see how the portfolios will perform.

In this simulation we assume for simplicity that all investments are equal in size, all pay an IRR of 15% and all have a 5% probability of defaulting, with $0 recovered in case of default.

We can now visualize how diversification affects our returns.

Notably, at any given portfolio size, the average return is the same (about 9.3% with these assumptions). But as we add more investments to our portfolio -- as we decrease its “name concentration” in financial jargon -- the variability of those returns go down, as the simulated returns cluster more closely around the expectation. As we diversify, our returns become more predictable.

Also note the dashed line representing a zero return in the chart. As we add more investments and the granularity of the portfolio increases, the probability that our returns will fall below this line -- i.e. that we will lose money -- decreases. For very granular portfolios, the probability of negative returns become almost negligible.^{1}

##### Measuring diversification

The above exercise is meant to illustrate a general dynamic, but it is simplistic in many ways. For example, the assumption that all investments are of equal size often fails to hold. Some portfolios are dominated by a few large loans -- they have high name concentration. How can we think of diversification when taking into account loans of different sizes?

One straightforward way to do this is to use the Herfindahl-Hirschman Index, or HHI. This index, which has long been used to measure market concentration by the U.S. Federal Reserve, is useful to gauge many kinds of concentration, including credit portfolio name concentration. In this context, we can think of it as an inverse diversification index.

The appeal of the HHI is its mathematical simplicity: it is simply the sum of the squares of each share of the whole. Put formally, it is:

where s_i is the share of the portfolio made up of each investment i. This means that the index ranges from close to zero for an “infinitely granular” portfolio to 1 for a portfolio with a single loan in it.

Applying this metric to liwwa, our overall portfolio has an HHI of .011. Since the meaning of this number is not very intuitive, it is often transformed into its inverse ( 1 / HHI ) which we can think of as the “effective number of loans” in the portfolio, accounting for their relative size.

By this metric, the effective number of loans in liwwa’s portfolio currently is 1 / .011 = 91. Of course, most of liwwa’s investors are not invested in all of our loans. The chart below shows the effective numbers of loans held by liwwa investors, expressed as a density distribution. liwwa users can download their portfolio data from our website to see how they compare.

liwwa encourages diversification by not requiring investments to meet some minimum limit -- unlike many other online lending platforms, we don't set minimum limits of $25-$100+ per individual investment. This means that even small liwwa portfolios can become well diversified over time.

Finally, we can look at the benefit of diversification in reality, by considering investments through liwwa's online platform. The chart below plots the returns of actual liwwa portfolios, held by our investors, against the effective number of loans in each portfolio. As predicted by the Monte Carlo simulation above, returns tend to cluster more tightly around the mean for well diversified portfolios -- in liwwa's case, around 13.9% IRR.

As illustrated above, investing over a larger number of campaigns will limit idiosyncratic risk in the portfolio. The systematic risk, however, remains. A strategy to limit some of the systematic risk in a credit portfolio is to invest across a range of industries and geographies. liwwa currently offers investment opportunities across a broad spectrum of industries in Jordan and the United Arab Emirates. If this investment strategy is employed, worsening macroeconomic conditions in one industry or geography will have a smaller effect on the returns of the overall portfolio.

Finally, to address diversification on a broader scale, investors should always consider investments through liwwa’s platform as one part of a larger diversified portfolio that might include stocks, bonds, CDs, mutual funds, real estate and/or other investment vehicles.

For any questions or comments regarding this article, please email us at investor@liwwa.com.

##### Further reading

Hirschman, Albert O. "The paternity of an index." The American Economic Review 54.5 (1964): 761-762.

"Studies on credit risk concentration ", Basel Committee on Banking Supervision, November 2006, http://www.bis.org/publ/bcbs_wp15.pdf

This simulation captures only idiosyncratic risks; even in diversified portfolios, systematic risk remains an issue. ↩