# Basel Capital

## How to Arbitrage Slotting Capital

Introduction
One of the options for allocating regulatory capital under Basel III and Solvency II is to use the "slotting" approach, whereby the capital for each asset is assigned according to a small number of slots, e.g., low, medium, and high risk. This creates specific behavior-incentives for the institutions under slotting and specific arbitrage opportunities for those institutions with more advanced approaches. This paper looks at the "game" set up by this set of incentives. The paper first summarizes the arbitrage opportunities and then explains the underlying rational. The opportunities are best explained on a graph.

Graph 1. Cost of Funds for Each Level of Measured Risk

In Graph 1 the x-axis is the riskiness as judged by the slotting criteria. The y-axis is the cost-of-funds. In Graph 1 the slotting cost-of-funds depends simply on the assigned capital per slot, multiplied by the required return on equity. For later discussion, the points on the steps are labeled as leading-edge and trailing-edge.

Graph 2. Range of Cost of Funds for Actual Risk

Graph 2 adds a range for the cost-of-funds. This range shows what the cost-of-funds (COF) would be if the risk was perfectly known. The true COF is different to the slotting COF for two reasons. Obviously the first reason is that the slots produce steps. The second reason is that the simplified risk assessments such as the typical slotting criteria do not capture all the possible risk variations within a deal: in a previous paper we demonstrated how the tenant, property and financial structures can produce great differences in risk for commercial property deals that seem to have identical risk according to conventional measures such as Loan [...]

June 22nd, 2016|

## LGD for Multi-Year Structured Loans

In a previous paper we discussed how to assign a single probability of default to represent the multi-year risk profile of a complex asset such as a commercial real estate (CRE) loan. In this paper we extend the method to cover Loss Given Default (LGD) and Exposure at Default (EAD). Such “compression” of the multi-year risk profile into scalars is required by conventions such as Basel capital calculations which are oriented to assets that can be defined uniquely by their year-one risk statistics, e.g., standard commercial loans and bonds.
In the previous paper we defined the representative one-year PD to be the year-one PD of a bond or commercial loan whose NPV of loss matched that of the CRE loan, assuming that the LGD and EAD were the same, i.e., such that:

$\sum\limits_{y=1}^M PD_{CRE,y}B_y = \sum\limits_{y=1}^M PD_{Bond,y}B_y$

Where:

$M$ is the number of years to maturity
$PD_{CRE,y}$ is the probability of default in year $y$ for the CRE loan
$PD_{Bond,y}$ is the probability of default in year $y$ for the standard bond
$B_y$ is the balance outstanding at default in year $y$

Now with this standard PD for the bond defined, we go one step further to define a single average LGD such that the net present value (NPV) of loss on the bond equals the NPV of loss on the CRE loan1:

$NPV(Loss) = \sum\limits_{y=1}^M EL_{CRE,y} = \sum\limits_{y=1}^M PD_{CRE,y}LGD_{CRE,y}B_y = \sum\limits_{y=1}^M PD_{Bond,y}\overline{LGD}B_y$

i.e.,

$\overline{LGD} = \frac{\sum_{y=1}^M EL_{CRE,y}}{\sum_{y=1}^M PD_{Bond,y}B_y}$

where

$EL_{CRE,y}$ is the expected loss for the CRE loan in year $y$[2. The [...]

1. For operational simplicity we again assume that the discount rate and interest income are negligible for this purpose.
April 15th, 2014|

## Rating CRE Loans Consistently with Commercial Loans

Rating CRE loans according to risk is a long-established practice in the financial industry, however it has become much more important because of the increasing requirements for quantitative risk reporting, e.g., for Basel capital and stress testing. Over the last few decades it has become conventional to rate loans according to their probability of default (PD) and loss given default (LGD). For simplicity, in this article we focus on the PD metric and how that should be interpreted for commercial real estate loans.
For standard retail and commercial loans and for corporate bonds it is assumed that there is a smooth progression in risk from the first year to subsequent years, therefore quoting the first year’s PD is sufficient to uniquely assign the loan to a particular rating or grade. However commercial real estate (CRE) loans are different because they are generally long-term loans with jagged risk profiles over time. The peaks and troughs of the profile are dictated by the deal’s structure and the interaction between the financing and features of the underlying property assets, for example expiration of swaps, lease breaks, rent renewals and refinancing patterns. A typical risk profile for a commercial real estate loan is shown below:

As an example of the disconnect between the first year PD and the overall risk, consider a property with a single large creditworthy tenant. This loan may have much lower risk in the first year than a property with 5 smaller units, however if that large tenant’s lease expires in year three, the risk will peak and may be much higher than that of the diversified property. Similarly an interest-only loan will have low PD in the first year, but a spike of refinancing risk [...]

March 18th, 2014|

## National Real Estate Investor interviews Risk Integrated on Basel III

All Publications >> Basel Capital

New lending practices due to Basel III will become embedded in commercial real estate in the U.S. in the next few years. Banks will come under more intense scrutiny about the risk of the loans on their balance sheets which will translate into requiring their borrowers to submit more frequent updates on property cash flows. Read Chris Marrison's views about it in a recent online article in National Real Estate Investor.

March 1st, 2011|

## Why Basel's Not Faulty

All Publications >> Basel Capital

Undesirable pro-cyclicality in banks' capital calculations should not be wholly blamed on the Basel II legislation. Online this month at Credit magazine, Chris Marrison argues that most of the pro-cyclicality is due to the models that banks choose for making the Basel II calculations.

January 15th, 2009|

## Basel II and the Sub-Prime Blow?

All Publications >> Basel Capital | Capital Management | Portfolio Management

Peter Andresén weighs the positive impact Basel II risk management procedures, already in place in most European banks, will have on their commercial real estate lending books. The Mortgage Finance Gazette features his discussion in their October 2007 issue.

October 18th, 2007|

## Project Finance Lenders Begin Implementing Basel II Regulations

All Publications >> Basel Capital

In a recent issue of Project Finance Magazine, Chris Marrison explains how Basel II regulation is influencing the competitive dynamics at project finance banks from origination onwards.

February 7th, 2007|

## Basel II - The Basic Equation

All Publications >> Basel Capital

In an article first printed in Infrastructure Journal in September 2006, Risk Integrated's Chris Marrison clarifies why the project finance departments at the largest, diversified banks are now pushing hard for the funding advantages attainable by achieving advanced Basel II compliance.

September 12th, 2006|

## Use of Risk Measurement Models in Specialized Finance

All Publications >> Basel Capital

Chris Marrison, chief executive of Risk Integrated, discusses measuring and mitigating risk in project finance deals in the Infrastructure Journal. He describes in detail the benefits of using simulation models over traditional cash flow models for calculating capital requirements for Basel II compliance.

September 6th, 2006|

## The Effect of Basel II on Project Finance

All Publications >> Basel Capital

This article first appeared in Infrastructure Journal, May 2006. Risk Integrated believes the importance and relevance of Basel II should be obvious to any business that considers profitability to be linked to cost of funds and pricing of capital.

May 26th, 2006|