littleoldlady
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Post by littleoldlady on May 9, 2017 9:21:01 GMT
Does anyone know how to work out the risk:reward function based on estimated default probabilities? I had a play around myself and was quite surprised or even alarmed by the results. Thinking of a well diversified portfolio of property loans paying 12% interest and a period of 12 months. I simply made a spreadsheet with 3 columns and eleven rows plus a total. Each row represents the effect of a loss in steps of 10 from 0 to 100%. The first column is the estimated probability of that degree of loss, the second the %loss and the third the expected amount of loss (col 1 * col 2). I then played around with col 1 until I reached a total expected loss of 12, the break even point. My first set of estimates produced an alarming loss of over 14. Eventually I managed to get it down to 12 by making more optimistic predictions, as shown below. Everyone can make their own guesses as to the probabilities of a loss at each level but ISTM from this simple exercise is that an investor probably needs at least 75% of his loans to repay in full in order to avoid a net loss, and over 90% to get a minimum rate considering the risk. Simply put if 24% of loans lose on average half then that's the 12% gone, or if 10% lose half that reduces the portfolio return from 12% to 7% (ignoring the complication that you will may not have got any interest on the failed loans - platform dependent) I am sure there must be more sophisticated methods known to some of you. ![]()  |
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yangmills
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Post by yangmills on May 10, 2017 10:51:18 GMT
Given nobody else has responded I'll take a stab. Your "back of the envelope" estimate is pretty reasonable. To get a bit more realistic, your can allow the loan to have multiple coupons (say monthly), allow the default to happen any time over the term, and assume some sort of lag between default and recovery, plus some risk-free discounting. You can then calculate the "fair value" NPV/expected return of the loan under given default and recovery assumptions. The sheet attached below does that. Example 1 is for a 12-month loan, paying monthly in arrears, with the default risk applied linearly over the term of the loan (say an SME loan for example). So for a 12% coupon, 24% default probability and 50% recovery, with 1 year time lag on recovery, the expected return is -2.91%. Example 2 is for an instant jump to default at term (say a bridge where all the interest was taken up front). Again, for a 12% coupon, 24% default probability and 50% recovery, with 1 year time lag on recovery, the expected return is -1.53%. In example 2, to generate a 7% expected return, you could tolerate a 13% default rate and 70% recovery etc. CreditRiskyBonds_TieOut.xls (43.5 KB) I used this sheet to tie out with the QuantLibXL credit default pricer that samford71 wrote, which it does precisely for these simple examples. I won't post his pricer since he's left the forum and that was his IP. My example sheet is far less flexible since it can't handle arbitrarily large portfolios of loans, with non standard cashflow structures, multiple default curves etc. But it could be easily changed to cope with a specific loan (say a 5-year amortizer or something). Hope this is useful. Back to lurking. |
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littleoldlady
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Post by littleoldlady on May 10, 2017 12:04:34 GMT
Thanks yangmills. Unfortunately my Jurassic era version of Excel will not open your spreadsheet, but it is encouraging to see that the examples you quote are in line with my rough estimates. ISTM that as a rough rule of thumb it is pointless investing in loans at 12% unless you are reasonably confident that 90%+ will repay in full. Could you plug in a few more figures and post the results here? |
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