Upper bounds on default probability for small cooperative loan books with no observed defaults

Savings and credit cooperatives (SACCOs) often hold small loan books with no formal defaults on record, for example because loans are fully collateralised or guaranteed by other members. A zero default count is not a default probability of zero. This technical note collects four standard ways to compute an upper bound on the default probability in that situation (the independent bound of Pluto and Tasche, a Bayesian bound with a uniform prior, a one-factor correlated bound and a beta-binomial bound), applies them to book sizes typical of an Ethiopian SACCO, and shows how much the answer depends on the correlation assumption. For 50 loans and no defaults, the 90% upper bound is 4.50% if defaults are independent and 5.2% to 9.2% under one-factor correlation of 0.03 to 0.16. Code and synthetic data: https://github.com/Nahombehailu22/sacco-credit-bounds (MIT licence; no member data).