Buenas a todos.
Nos adentramos más en la cantidad e préstamos necesarios para una óptima diversificación y lograr una reducción máxima del riesgo.
En el estudio "Risk Reduction and Portfolio Size: An Analytic Solution,” de Elton and M. J. Gruber de 1977 llegaron a la conclusión de que con una cartera de 30 activos
http://www.firstadvisorscapital.com/p/how-many-holdings
El estudIo en cuestión de Elton and M. J. Gruber:
https://www.google.es/url?sa=t&source=web&rct=j&url=http://pages.stern.nyu.edu/~eelton/papers/77-oct.pdf&ved=0ahUKEwiFssTcp6LWAhXL0RoKHXwoCNkQFggpMAA&usg=AFQjCNExcOpeJZrh-w37DrL8CwROVXGLwQ
Sobre esa base Lendingrobot realizó un estudio sobre la cantidad de préstamos a partir de la cuql en se llegaría a tener una rentabilidad positiva en la práctica totalidad de prestamos; la conclusión fué que el número mágico era 146.
In previous SeekingAlpha articles, we analyzed the
financial returns of Peer Lending, and the
type of risks associated with this asset class. By far, the biggest risk is defaulting: the borrowers simply stopping to pay back a loan. The mantra in Peer Lending is that since an investor puts only small chunks of money, into many loans, that provides diversification and lowers this risk considerably. ‘Does it?’ is the question we’re trying to answer below.
As previously, our data analysis is based on LendingClub’s historical data, which is available for anybody to peruse from the
Lending Club website. As of January 2013, more than 230,000 loans have been issued. Unfortunately, most of them cannot be taken into account since they’re too young to have been fully paid (or ‘reach maturity’, in Bonds terms). If we restrict the dataset to loans that are old enough to have reached maturity, it leaves 17,558 36-months loans, issued between June 2007 and January 2011.
We can calculate the Return on Investment of a loan with the following formula:
where p is the sum of payments made to investors and c is the cost of the loan, or amount lent by investors. Both values are given by Lending Club’s historical data, as ‘Total Payment to Investors’ and ‘Amount Funded by Investors’, although we have to discount the ‘Total Payment to Investors’ by 1% to take into account the Service Fees kept by Lending Club.
When calculating the Return on Investment for multiple loans, we simply sum the payments and costs of all the loans’ investments:
We’ll consider the returns between two loans to be independent of each other, which seems acceptable since a) default from a man in Nevada who borrowed money to fix his car is unlikely to affect the probability of default from a woman in Florida who wanted to pay back her credit card, b) historical data (for instance from S&P Experian Consumer Credit Default indices) shows a close-to-zero beta, which means defaults on consumer credit loans are not correlated with market conditions.
If returns are independent, returns will converge toward the total market average as the number of invested loans increases. If you want to show off at a cocktail party, you can even explain it’s due to the
Central Limit Theorem, and that the returns follow a normal distribution.
Considering the distribution is normal, the ’Three Sigma Rule’ tells us that almost all the outcomes (99.7% of them to be precise) are comprised between the average minus 3 times the standard deviation and the average plus 3 times the standard deviation.
We use a Monte-Carlo Method to calculate those numbers and measure how diversification reduces risks. The Monte-Carlo Method is just a fancy way of saying ‘repeat random trials a lot of times’. We’re first investing in a single loan at random, repeating the experiment 50,000 times to estimate the average return and standard deviation (or how much the results vary). Then we repeat the process by investing in 2 loans, 3 loans and so on…
Investing in a single loan at random on Lending Club gives an average return of 5.75%, with a standard deviation of 24.35%. Therefore, in virtually all cases, our theoretical return for investing in a single loan would have been between –67.3% (5.75% – 3 * 24.35%) and 78.8% (5.75% + 3 * 24.35%). And the two words to characterize such an investment are: insanely risky! In practice, the returns are bounded by historical data: the best loan in Lending Club history had a return of 37.9% (sic).
But, as we increase the number of loans, the risk goes down precipitously:
Graph
Number of loans
Average Return
Standard Deviation
Lower Bound
Upper Bound
Best case
1
5.2033%
25.1532%
–70.26%
80.7%
37.9%
2
6.4844%
18.3609%
–48.60%
61.6%
37.9%
3
6.8782%
15.2617%
–38.91%
52.7%
37.7%
4
6.6811%
14.1559%
–35.79%
49.1%
37.4%
5
6.9942%
12.4705%
–30.42%
44.4%
37.1%
10
7.0534%
8.8711%
–19.56%
33.7%
36.3%
20
7.1361%
6.4418%
–12.19%
26.5%
35.2%
50
7.1726%
4.0416%
–4.95%
19.3%
33.3%
100
7.1784%
2.8620%
–1.41%
15.8%
32.0%
145
7.1700%
2.3919%
–0.01%
14.3%
31.3%
146
7.1597%
2.3790%
0.02%
14.3%
31.2%
200
7.1815%
2.0266%
1.10%
13.3%
30.36%
500
7.1782%
1.2646%
3.38%
11.0%
27.8%
With 146 loans, the total returns is positive in (almost) all the cases. And that’s our magic number. If one invest $25 per loan, it means the minimum amount of money to be ‘be sure’ not loose money is $3,650.
Returns sharply converge toward the average, which is 7.18% over the period. As a comparison, the average yearly return for 10-year T-bonds from 2007 until now is 5.3%. (source: Federal Reserve database), and is likely to be in sync with ETFs like IEF (iShares Barclays 7–10 Year Treasury Bonds)
Of course, past performance is never a guarantee of future results. And nothing proves the returns are independent, but we think that’s a reasonable assumption. Since investing in 146 loans on Lending Club requires a very low amount of capital, Peer Lending seems to keeps in promises of affordable diversification and low-risk investment.
http://blog.lendingrobot.com/research/146-the-magic-number-for-lending-club-investments/
Desde luego que para tener en cartera 146 préstamos hay que diversificar entre distintas plataformas.
Saludos matemáticos y diversificados.
