Portfolio Theory and Banks

by Eric Brennan


Over the years competition in the financial industry has been very high.  Banks have been competing harder over market shares and profits.  These firms have of late been facing a very unique challenge; how to extract high levels of profit while still maintaining their foundations as lending institutions.  Lending is not a very profitable business, the risk of default coupled with the competition driving down market prices have made lending a less attractive enterprise.  Therefore some banks are trying to concentrate on their more profitable activities (i.e. advisories, debt and equity sales, mergers and acquisitions).   But to be able to extract this sort of business requires banks to engage in loans.  Without loans customers have no incentive to do business with them, since one of their primary needs is to finance their commercial activities through debt.  Portfolio theory gives these lending institutions a tool to minimize the risks and hazards of lending. 

Portfolio theory was first published by Fischer Black and Myron Scholes in 1973.  This model provided banks with a strategy on how to diversify their loans and investments.  Before this, banks had no real investment strategy and their only option was to obtain as much collateral as possible and make default an unattractive option.  Portfolio Theory allows companies or investors to diversify their investment so to minimize risk and maximize gain.  The principle behind the Black – Scholes model is to diversify your equity so that your lowest risk bond produces the same risk as your highest risk investment.  When your investments have reached this equilibrium, then risk minimization has been achieved.[1]  



What is the Black - Scholes model?  The model also called portfolio theory works under the following assumptions: 1) Price of the underlier is lognormally distributed 2) No transaction costs 3) Markets trade continuously 4) Risk-free rate is constant and the same for all maturities.[1]  The model was first used for simple put and call options and now has been expanded for use with other financial instruments.  This model is a mathematical model and certain variables are needed for the formula to work.  These variables are the stock price, exercise price, time to maturity, volatility, and price of a discount bond that matures when the option does.[2]  These calculations are generally done on computers using portfolio model software, and they are calculated continuously to insure up to date information. 




The first step toward modeling under these principles is assessing the default risks of the current companies you are invested in.  This is done by looking at the amount of leverage a company has acquired versus its asset value.  Once the companies’ asset value is no longer greater to or equal to its debt then default is probable.  It is also important to know the volatility of the investment.  Volatility is how subject to change their asset value is.  It’s important to know how volatile the industries assets are in general (i.e. tech industries are more volatile then food and beverage industries).[1]  Now volatility basically converts into the risk involved and how many movements their value would need to take for the company to default.  So if they are worth $100, leveraged $25, and their asset volatility is $25 then they have to move by 2 standard deviations to hit default level.  It is also important for banks to know their exposure to the companies that they’re invested in so the firm has a general idea of how much it stands to lose should one of these companies go under.  Now one must measure the diversification of the portfolio.  This is done by “specifying the range and likelihood of possible losses associated with the portfolio.”[2]  It also must be known if any of the investments correlate with one another (i.e. if one company defaults will that hurt another of your investments and if so how much.).  In this increasingly interconnected economy this model’s strength can be very important.  This is generally done by calculating economic factors that would affect all business rather then just a handful.  Also it is important for a bank to have an expectation of losses.  The model also predicts your losses, and normally if it is diversified you may have a large risk of small losses while a small risk of large defaults.  This doesn’t mean it’s well diversified.  An example of a well diversified fund is “Portfolio A is better diversified than portfolio B if the probability of loss exceeding a given percent is smaller for A than for B, and both portfolios have the same expected loss.”[3]  It is also important to know the value of the loans that are in the firm’s portfolio.  While most cannot be sold, it still should be known how much they’re worth.  This can be determined by comparing the loans acquired with what that companies bond would be worth on the open market.  It is also worth it to note that bank loans are more then just their face value; it is a link through which the two firms can do further business and become partners. 


[3] Ibid


That is what the components of the model are and how the fund is analyzed.  This is also how the portfolio is managed, because Banks get the capital to purchase debt from other institutions within the bank, such as what it takes in from deposits, fees on the various services it renders, and even from outside sources.  The firm must manage this portfolio in such a way that return is high, while risk is kept to a minimum.  Now the debt the bank has acquired has value.  The value contributed by the rest of the bank should be equal to the excess of the market value of its assets over the market value of its borrowings.[1]  The objective of this fund management is to maximize the value of the money you invested into the fund.  Two other objectives that are necessary for a successful portfolio and should be complementary, are to get maximum diversification and get capital adequacy.  Capital adequacy means that you have enough equity to support your debt with low levels of risk.  If the bank’s debt is greater then its equity value the probability is that default will occur.  So with these tools a bank or other financial institution may minimize their exposure to risk and maximize the profits acquired from lending. 

[1] Ibid


Portfolio theory is an integral part of today’s financial industry and has provided banks with a very important tool in combating defaults and profit losses.  Unfortunately, even these tools aren’t perfect and the elimination of risk is an impossibility in this ever changing world.  But given future refinement of this model along with further computerization, experience and new tools, default risk my become even further mitigated. 









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