Plan sponsors participating in securities lending programs have often preferred to accept government debt securities as collateral for their loans, reasoning that these instruments exhibit less volatility and provide better credit quality. In recent years however, compelling arguments have been made that diversifying collateral pools by accepting(for example)equities, can reduce market risk by improving the correlation between loaned securities and collateral. It is important to analyse what affects a securities lending portfolio’s value at risk(VaR), measure its sensitivities to key variables, and suggest that there is a “right” mix of equity and bond collateral to minimize risk.(VaR estimates the probability of portfolio losses based on the statistical analysis of historical price trends and volatilities).

Securities lending(SL)is a temporary loan of securities (fixed income or equities)from one party(the lender) to another(the borrower). In exchange for the loan of the securities, the lender receives collateral in the form of cash or securities. In typical non-cash SL transactions, the market value of the collateral securities exceeds that of the loaned securities by a predetermined margin. In the event that a borrower defaults, the collateral is sold and the proceeds are used to repurchase the loaned securities. Price movements of the securities can cause situations where the cash proceeds from the sale of the collateral are insufficient for purchasing the loaned securities, resulting in a loss for the lender and/or the lending agent.

The risk of potential loss is determined primarily by price volatility, and the correlation between loaned securities and collateral. Generally, the higher the correlation between loans and collateral, the lower the risk to the overall securities lending portfolio. If the market value of the loans and of the collateral move in the same direction, it is likely that the margin will remain positive and there will be no resulting loss. Therefore, the composition of the collateral portfolio is a key determinant when measuring the size of the risk of a SL program. Two other determinants are the margin level and time required to liquidate the collateral and repurchase the loaned securities.

In order to illustrate these concepts, three types of loans within a securities lending program will be reviewed. They are: bond loans collateralized by bonds(B:B), equity loans collateralized by bonds(E:B)and equity loans collateralized by equities(E:E).

THE METHODOLOGY
A historical simulation method was used to estimate VaR over a five-year period. The simulation depicts the probability distribution of the difference between the value of collateral and the value of the loans(C – L)at different confidence intervals. The control variables are: 1)reaction time or delay in the collateral’s liquidation and replacement of loaned securities, 2)equity as a percentage of total value of collateral and 3)margin level.

Case 1: equity loans
Equities can be addressed by analysing three variations of the same portfolio. The loan portfolio is all equities and is the same for all three cases and in each case the margin level is set at 105%. The variation lies in the asset class mix of the collateral.

Portfolio A: Collateral is 20% equities and 80% bonds
Portfolio B: Collateral is 100% bonds
Portfolio C: Collateral is 100% equities

The return characteristics of the securities that make up the collateral are very different. Equities are more volatile than bonds. Indeed, the distribution of returns for equities is flatter and has a fatter tail(a greater likelihood of events that will deviate from the mean) than does that of the bonds. In Portfolio C, equities display a relatively high positive correlation(0.61) with respect to the loaned securities. In contrast, bond collateral and equity loans in Portfolio B maintain a low and negative correlation(- 0.28)(see “Case 1,” above).

Upon initial observation of all three portfolios, we draw a conclusion that the longer the reaction time, the higher is the value at risk. Reaction time is the time it takes to liquidate the collateral in order to repurchase the loaned securities in the unlikely event of borrower defaults. If a borrower defaults, there is a risk that the market value of the loans will go up relative to the market value of the collateral. The longer it takes to liquidate the collateral and buy back the loaned securities, the higher the risk of adverse movements.

AN OPTIMAL MIX?
For equity loans, equity collateral is better correlated than bonds. However, as the weight of equity collateral increases, the collateral volatility also increases, which in turn drives up the overall risk of the SL portfolio. Thus, there is a trade off between correlation and volatility. This suggests that there is an optimal mix of equity and bonds that minimizes risk. The analysis of VaR supports this hypothesis. The relationship between the percentage of equity in the collateral mix and VaR is illustrated in “VaR and percentage of equity,” on the following page and can be characterized by a U-shaped curve. VaR as percentage of the market value of the loans is represented by the Y axis whereas the percentage of equities in the collateral is represented in the X axis. Through a process of trial and error, we can determine the mix of collateral that minimizes VaR. For example, for the sample portfolios using a five-day reaction time VaR reaches zero when the percentage of equity in the collateral portfolio is approximately 35%, and increases again when it is above 55%.

Case 2: introducing bond loans
We can apply the same optimization process described in Case 1 to determine the right mix of collateral of a loans portfolio that includes both bonds and equities. In the general case, we would have three types of loans: equity loans collateralized by equities(E:E); equity loans collateralized by bonds(E:B)and; bond loans collateralized by bonds (B:B).

The margins for equity loans collateralized by equity (E:E)and by bonds(E:B)are set at 105%, just as in the first case. Because bonds are generally less volatile than equity, the margin for bond loans collateralized by bonds(B:B)can be lowered from 105% to 102 per cent with a negligible impact on the portfolio’s risk.

If the proportion of B:B is fixed at 72% of all the portfolio, we can use the same optimization process involving trial and error that we used previously to determine that an E:E mix of 9% and an E:B mix of 19 per cent minimizes VaR for this sample portfolio.

CONSIDER THIS
When the collateral for bond/equity loan portfolios contains a mixture of bonds and equities, the risk of an SL portfolio can be reduced significantly. This is due to improved correlation between collateral and loans. However, it has also been shown that we cannot indefinitely increase the weight of equity collateral because after reaching an optimal level, subsequent increases in the amount of equity collateral tend to impair VaR as increased volatility outweighs the better correlation.

Furthermore, VaR of a SL portfolio is sensitive to time and hence, reaction time also impacts the right mix of collateral. Through an optimization process it has been shown that for any given margins and reaction time, there is a right mix of equity that minimizes VaR for the sample portfolios.

Clearly it is important for plan sponsors to engage a lending agent who understands the importance of collateral composition and its effect on risk. These findings also underscore the value of approving flexible collateral guidelines that allow the agent lender to have appropriately structured collateral pools that help minimize the risks associated with securities lending.

James Slater is senior vice president of capital markets. Gabriel Villegas is a business analyst. Both are with CIBC Mellon in Toronto. james_slater@cibcmellon.com; gabriel_villegas@ cibcmellon.com

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