# What happens if banks invest in funds?

3 januari 2014 1 reactie

An interesting new Basel Committee paper (*Capital requirements for banks’ equity investments in funds*, December 2013) presents the framework for calculating the capital requirement for banks’ equity investments in funds. The framework intends to achieve a more risk-sensitive capital treatment for banks’ equity stakes in funds.

This risk-sensitivity is implemented by making the capital requirement dependent on the risk of the fund’s assets and its leverage.

The framework consists of three approaches, the “look-through approach”, the “mandate-based approach” and the “fall-back approach”. The first approach is the most granular and risk-sensitive and we will focus on that approach in this post.

The *look-through* *approach* requires a bank to risk weight the fund’s assets as if the exposures were held directly by the bank. Hence, it can only be used if the bank has sufficient information on the underlying exposures of the fund.

However, the capital requirement is also dependent on the leverage of the fund.

For the application of the *look-through approach* leverage is calculated as the fund’s ratio of total assets to total equity. The leverage adjustment is applied to the capital requirement as follows:

After calculating the total risk-weighted assets of the fund according to the LTA or the MBA, banks will calculate the average risk weight of the fund (Avg RWfund) by dividing the total risk-weighted assets by the total assets of the fund. Using Avg RWfund and taking into account the leverage of a fund (Lvg), the risk-weighted assets for a bank’s equity investment in a fund can be represented as follows:

RWAinvestment = Avg RWfund * Lvg * equity investment

The idea is of course that the default risk of the fund is larger if the fund is highly leveraged and is less able to absorb shocks. The factor *Avg RWfund * Lvg* is capped at 1250%, meaning that, after taking 8% of the RWA as the capital charge, the capital charge is capped at 100% of the investment.

*Example*

Suppose that the average risk weight of the fund is 50%, leverage 20 (equity is 5% of total assets) and the bank’s equity investment EUR 20K, the RWA of the investment equals min(50% * 20; 1250%) * EUR 20K = EUR 200K. The capital charge equals EUR 16K.

## Does the risk increase proportionally to the fund’s leverage? Analysis with the help of the Merton framework

Although the formula is easy to apply, it is not obvious why the risk would increase proportionally with the leverage ratio. In order to analyze this formula we compare it to the Merton model in which the equity is seen as a call option on the bank’s asset value. The option is only ‘in the money’ if the assets earn sufficient return after paying off the debt holders.

Below we will compare the equity risk that is determined by the capital charge using the *look through approach* to the probability that the call option is not exercised, i.e. the probability that the equity stake turns out to be worthless according to the Merton framework.

We will calculate the capital charge for an equity stake in a high-yield fund.

- The capital charge is calculated for average risk weights between 50% (A+ to A- bonds) and 150% (below BB- bonds).
- The fund’s percentage equity to total assets ranges between 1% and 90%.

The Merton framework uses a total assets volume that is standardized to 1.

- The current stock price
*S*of the call option equals the current asset value, so it is set equal to 1. - As stated above, the fund’s percentage equity to total assets ranges between 1% (high leverage) and 90% (low leverage).
- The strike price is equal to 1 minus the fund’s percentage equity to total assets, so it ranges between 10% (low leverage) and 99% (high leverage). The strike price is equal to the percentage debt to total assets. If the stock price is above the strike price, i.e. if the assets are worth more than the fund’s debt, the call option is ‘in the money’ and the equity has a positive value. However, if the asset value is below the percentage debt to total assets, the fund defaults and the equity, and hence the call option, is worthless.
- A risk-free rate of 4% is assumed.
- A volatility of 20% is assumed, in accordance with the high-yield profile of the fund (risk weight 50% and higher).

## Comparison of the risk-sensitive Regulatory Capital levels with the fund’s default risk

Below we show the call option price against the percentage equity to total assets. Note that the option price is above the percentage equity to total assets (expressed with the help of the red line). The difference between the option price and the percentage equity to total assets converges to zero as the fund progresses to a 100% equity funding situation. This is an important outcome. *It shows that equity holders do not have an incentive to reduce the leverage of the bank, since the value of their call option on the bank’s assets increases slightly less than the percentage equity to total assets. *

The figure illustrates that the option value of the equity is most valuable at low solvency levels.(1)

In the figure below we show the regulatory capital (8% of RWA) according to the *look through approach* for several average risk weights (50%, 70%, …, 150%). We compare the outcomes of the risk capital to the investment’s default risk as measured by the Merton approach. Within the Merton approach, the probability of *not* exercising the option, i.e. the probability that the equity investment turns out to be worthless, equals N(-d2).

From the figure we can conclude that the regulatory capital formula follows more or less the shape of the probability to not exercise in the Merton approach. Also, the capital requirement is conservatively above this probability for risk weights below 150% (corresponding to below BB- bonds).

My conclusion is that, although the multiplication with the leverage ratio may seem odd, the resulting regulatory requirement for banks’ high-risk equity investments in funds turns out to be reasonable if the fund’s assets comprise externally rated high-yield corporate debt. However, some red flags remain. If (for whatever reason) the risk weight of the fund’s assets is underestimated, the *look through approach* may turn out to be too optimistic. It relies heavily on an adequate rating. Also, it does not take other relevant risk factors into account such as the concentration of the fund’s assets or the quality of the fund’s management.

(1)See M.J.P. Lubberink, A primer on regulatory capital adjustments, forthcoming, SSRN http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2305052

## Appendix: Option theory

The value of a call option c is S(0)*N(d1) – K*exp(-rT)*N(d2).

In this formula N(d2) is the probability to exercise the option. The probability to *not* exercise the option is N(-d2). In the Merton approach, this is equal to the probability that the equity turns out to be worthless. Hence, N(-d2) is an estimate of the firm’s PD. Sometimes the Black-Scholes formula is enhanced to reflect the asset return drift instead of the risk-free rate.

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This is an interesting post by Marco Folpmers: What happens if banks invest in funds?