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Analytical Solutions for Expected Loss and Standard Deviation of Loss with an Additional Loan

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  • Satoshi Yamashita
  • Toshinao Yoshiba

Abstract

We evaluate the expected loss and the standard deviation of loss of a bank loan, considering the bank’s strategic control of the expected return on the loan. Assuming that the bank supplies an additional loan to minimize the expected loss of the total loan, we provide analytical formulations for the expected loss and the variance of loss with bivariate normal distribution functions. Using a given expected growth rate and interest rates, two thresholds for the asset/liability ratio can specify three cases. The bank supplies an additional loan to decrease the expected loss in two cases: (i) the asset/liability ratio of the firm is low, and its expected growth rate is high; and (ii) the asset/liability ratio of the firm is high, and the lending interest rate is high. The bank maintains the current loan amount when the asset/liability ratio lies between the two thresholds. Depending on the bank’s strategy, the bank can decrease the initial expected loss of the loan. Conversely, the bank would face a greater risk of the standard deviation of loss. Copyright Springer Japan 2015

Suggested Citation

  • Satoshi Yamashita & Toshinao Yoshiba, 2015. "Analytical Solutions for Expected Loss and Standard Deviation of Loss with an Additional Loan," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 113-132, May.
    • Handle: RePEc:kap:apfinm:v:22:y:2015:i:2:p:113-132
    DOI: 10.1007/s10690-014-9196-5
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    References listed on IDEAS

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    1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    2. Jon Frye, 2000. "Collateral damage detected," Emerging Issues, Federal Reserve Bank of Chicago, issue Sep.
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    More about this item

    Keywords

    Expected loss (EL); Exposure at default (EaD); Loss given default (LGD); Probability of default (PD); G21; G32; G33;
    All these keywords.

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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