Pricing liquidity · RiskAtoms Academy

By the end you will be able to

1Explain what funds transfer pricing is for: making each business pay for the liquidity it uses and be paid for the liquidity it brings.
2Distinguish the liquidity tenor from the interest tenor, and explain why charging liquidity at the reset date makes long lending look too profitable.
3Build a term liquidity premium curve with e and price a loan with continuously compounded rates.
4Cost the liquidity buffer, share it out by stressed outflows, and credit stable deposits.

Why it matters

In December 2011 the Financial Stability Institute of the BIS published a survey of 38 large banks in nine countries on how they priced liquidity inside the bank. Many had no liquidity transfer pricing policy at all. Some charged their businesses nothing for liquidity on some activities; others charged everyone one average rate, which neither penalised lending for long nor rewarded raising money for long, and did not move when markets did. In such a bank a trading desk that bought illiquid assets funded overnight, or a business that wrote liquidity lines, showed a profit that ignored the cost of the cash the bank might need for it. Prices steer behaviour. If liquidity is free inside the bank, the bank will use too much of it.

Core explanation

An internal market for money

Illustrative dataRiskAtoms Bank plc's liquidity book

A £67bn balance sheet on one made-up reporting date, in pounds: every line's contractual maturity, its HQLA level, LCR rate and NSFR factors, the undrawn facilities and collateral triggers, and a daily 90-day stress test in three scenarios. The numbers are round illustrative values, not any bank's data, and the cash flows are principal only (no interest). The same book runs through every lesson in Module 3.5, so the figures agree.

Extra for this lesson: an illustrative funds transfer pricing curve (a SONIA base curve starting from the 4.00% policy rate of L3.5.02: How banks fund themselves, plus a term liquidity premium), what each HQLA level earns, and behavioural lives for the deposits. The buffer and the LCR outflows that drive the charges are the book's own.

Every bank has businesses that lend and businesses that raise money, and they are rarely the same people. Funds transfer pricing (FTP) puts the treasury in the middle: it buys every pound a deposit-taker raises and sells every pound a lender lends, at internal prices. The interest rate risk moves to the treasury, where L3.6.01: What ALM does takes it up. The liquidity risk is priced too, in three parts.

ExploreWhat the treasury charges a lender

Click a box to see what happens there.

Base rate

The risk-free rate for as long as the loan's rate is fixed: here the SONIA swap curve. A loan that resets every three months pays the three-month base rate, 3.946%; a five-year fixed loan pays the five-year rate, 4.207%.

The curve

The bank's curve, continuously compounded, with the annual equivalent of each FTP rate:

Tenor	Base (SONIA)	Liquidity premium	FTP rate	FTP, annual
1m	3.930%	4.26bp	3.973%	4.053%
3m	3.946%	12.37bp	4.070%	4.154%
6m	3.969%	23.57bp	4.205%	4.294%
1y	4.011%	42.86bp	4.439%	4.539%
2y	4.079%	71.59bp	4.795%	4.912%
3y	4.133%	90.84bp	5.042%	5.171%
5y	4.207%	112.41bp	5.332%	5.476%
7y	4.253%	122.09bp	5.474%	5.626%
10y	4.289%	127.62bp	5.565%	5.723%

In practice the premium is read from what the bank actually pays: the spread of its own senior bonds, certificates of deposit or term deposits over the swap curve at each tenor. It is the marginal cost, what the next pound of term funding would cost, not the average of what the bank raised years ago.

The cost of the buffer

L3.5.06: The liquidity buffer built a buffer of £13.7bn after haircuts, £14.5bn at market value. The bank funds it with term money, here for one year at 4.439%, because a buffer funded overnight would leave in the very stress it is there for. The assets earn less than that:

Holding	Value	Earns	Funded at	Cost a year
Level 1 (reserves, gilts)	£11.5bn	4.011%	4.439%	£49.29m
Level 2A	£2.0bn	4.261%	4.439%	£3.57m
Level 2B	£1.0bn	4.411%	4.439%	£0.29m
Total	£14.5bn			£53.14m

£53.14m a year is the price of being able to survive 30 days of stress. The LCR's outflows, £10.08bn in L3.5.07: LCR and NSFR in practice, say who needs it, so each business pays in proportion:

Business	LCR outflows	Share	Buffer charge a year
Retail banking	£2.28bn	22.6%	£12.02m
Corporate banking	£3.88bn	38.5%	£20.46m
Markets and treasury	£3.92bn	38.9%	£20.67m

Markets and treasury pays the most for the least balance: deposits from other banks run off at 100% in the LCR, so they carry 42.18bp a year of buffer cost, against 2.64bp on insured current accounts.

Credit for stable funding

Deposit	Balance	Behavioural life	Credit	Buffer charge	Net	A year
Stable retail deposits (insured current accounts)	£22.0bn	4.0 years	103.75bp	2.64bp	101.12bp	£222.5m
Less stable retail deposits (instant-access savings)	£10.0bn	1.5 years	58.65bp	5.27bp	53.38bp	£53.4m
Operational deposits from companies (payments and cash management)	£5.0bn	1.0 years	42.86bp	13.18bp	29.68bp	£14.8m
Other corporate deposits	£5.5bn	3 months	12.37bp	16.10bp	−3.73bp	−£2.1m
Deposits from banks and other financial institutions	£3.0bn	1 months	4.26bp	42.18bp	−37.92bp	−£11.4m

Current accounts are the bank's best funding: credited 101.12bp net, £222.5m a year to the retail business. Bank deposits are the worst: the premium for one month does not cover the buffer they need, so they cost the business that takes them.

Four ways to get it wrong

The formal version

Rates are continuously compounded (L1.3.05: Continuous compounding): £1 lent at $r$ for $T$ years grows to $e^{rT}$ . For a product with interest tenor $T_i$ , liquidity tenor $T_\ell$ and contingent need $h$ (pounds of buffer per pound lent):

\begin{aligned} \text{LP}(T) &= \text{LP}_\infty\big(1 - e^{-T/\tau}\big) \\ \text{FTP} &= r_{\text{base}}(T_i) + \text{LP}(T_\ell) + h\,c \\ B &= \textstyle\sum_k V_k\,\big(\text{FTP}(1) - r_{\text{base}}(1) - s_k\big) = \text{£}53.14\text{m} \\ c &= \frac{B}{\text{HQLA}} = \frac{\text{£}53.14\text{m}}{\text{£}13{,}700\text{m}} = 38.79\text{bp} \\ \text{charge}_j &= B \times \frac{\text{outflow}_j}{\sum_i \text{outflow}_i} \\ r_{\text{annual}} &= e^{r} - 1 \end{aligned}

$V_k$ is the market value held at HQLA level $k$ and $s_k$ what it earns over the base rate (0, 25bp and 40bp here); $B$ is the buffer's cost a year and $c$ its cost per £1 of HQLA. On this curve $\text{LP}_\infty = 1.30\%$ and $\tau = 2.5$ years: the premium reaches 63% of its long-run level at 2.5 years and 86% at five.

Try it

Move the long-run premium and how fast it builds, as if the bank's credit spreads had widened or narrowed. Pick a product to see what it is charged or credited.

Try itPrice liquidity with a transfer pricing curve

Long-run liquidity premium LP∞130bp

How fast it builds, τ2.5 years

Base rate (SONIA OIS)FTP rate = base + LP

Product

FTP charge5.078%

Net margin after FTP86.8bp

Base rate at the interest tenor3.946%

Liquidity premium, 5 years112.4bp

Contingent charge (undrawn line)0.8bp

Customer rate5.946% (6.127% a year)

Margin if LP were priced at 3 months187.6bp

Liquidity cost over 5 years, £100m£5.78m

Cost of the buffer a year£53.1m

Per £1 of buffer38.8bp

Set LP∞ to zero: the loan's margin looks more than a percentage point better and the buffer seems to pay for itself, which is roughly how many banks priced before 2008. Raise τ and the premium builds more slowly, so short funding looks cheap and long funding less so.

Worked example

Pricing a five-year corporate loan

The relationship manager's deal, through the treasury

Step 1 of 5

1
The deal
A company borrows £100m for 5 years at a floating rate reset every three months, with a further £20m committed but undrawn. The relationship manager quotes three-month SONIA plus 2.00%: $3.946\% + 2.00\% = 5.946\%$ continuously compounded, or 6.127% a year.

What the treasury notes

Five-year floating loan, £100m drawn and £20m undrawn: FTP 5.078% (base 3.946%, liquidity 112.41bp, contingent 0.78bp). Customer rate 5.946%; net margin 86.82bp. Approve on liquidity grounds; credit and capital to follow.

Regulatory lens

Basel. Principle 4 of the 2008 Principles for Sound Liquidity Risk Management and Supervision asks banks to build liquidity costs, benefits and risks into internal pricing, performance measurement and new product approval for all significant activities, on and off the balance sheet, so that each business line's incentives match the liquidity risk it creates for the bank as a whole.

Europe. The Committee of European Banking Supervisors set out the detail in its guidelines on liquidity cost benefit allocation of 27 October 2010: the methodology should be approved by the management body, compensate the providers of liquidity and charge the users, use the liquidity tenor rather than the interest rate tenor, reward deposit gatherers for stable liabilities, and allocate the cost of the buffer to the business units and products that generate the need for it. Supervisors review FTP as part of the bank's internal liquidity assessment, the ILAAP, covered in M4.5: Liquidity and IRRBB regulation.

Spark Atoms

Spark AtomFree money on the trading floor

Before 2008 a trading desk at many banks could buy a long-dated, hard-to-sell security and fund it at the overnight rate inside the bank. The carry looked like profit. When markets froze, the treasury had to fund the position for as long as it could not be sold, and the “profit” turned out to be an unpaid liquidity premium.

Spark AtomWhy e?

This lesson builds its FTP curve in continuously compounded rates because they add up across tenors and discount factors multiply cleanly:

e^{-r_1 T_1} \times e^{-f (T_2 - T_1)}

. The shape

1 - e^{-T/\tau}

is the same one that describes a capacitor charging or a drug reaching its steady level: fast at first, then flattening.

Key takeaways

Funds transfer pricing charges each business for the liquidity it uses and credits it for the liquidity it brings, so profit reflects funding risk.
The base rate follows the interest tenor; the liquidity premium follows the liquidity tenor. Mixing them made long lending funded short look profitable.
On this curve a five-year floating loan pays 112.41bp for liquidity, not 12.37bp; its margin is 86.82bp, not 187.63bp.
The buffer costs £53.1m a year (38.79bp per £1); it is charged by share of LCR outflows, and undrawn lines pay their part.
Stable deposits earn a credit at their behavioural life: current accounts 101.12bp net, £222m a year to retail.

Reaction

Check what stuck

Question 1 · objective 2

A five-year corporate loan's rate resets every three months. Which tenor should set its liquidity premium?

AThree months, because that is when the rate resetsBFive years, because the bank's money is tied up until the loan is repaidCOvernight, because the bank funds itself overnightDOne year, because that is the buffer's funding tenor

Question 2 · objective 3

A bank's term liquidity premium is LP∞ (1 − e^(−T/τ)) with LP∞ = 1.20% and τ = 2 years. What is the premium for two-year money, in basis points?

bp

Question 3 · objective 3

An FTP curve quotes 5.00% continuously compounded. What is that as an annual rate, in %?

%

Question 4 · objective 4

A bank's buffer costs £50m a year. One business line causes £1,000m of the bank's £10,000m of 30-day stressed outflows. What is its share of the cost, in £m a year?

£m

Question 5 · objective 4

Why does a good FTP framework pay a credit to the retail branch network for insured current accounts?

ABecause current accounts pay no interestBBecause they behave like long-term funding, which would otherwise cost the bank a term liquidity premium, and need little bufferCBecause regulators require deposits to be credited at the policy rateDBecause the branches would otherwise close

Glossary

Funds transfer pricing: Funds transfer pricing (FTP): the internal prices at which a bank's treasury lends money to the businesses that use it and pays for money raised by the businesses that gather it, so that each product's profit reflects its funding and liquidity cost.
Term liquidity premium: Term liquidity premium: what the bank pays, over the risk-free rate, to borrow for a given term rather than overnight. It rises with the term and with the market's doubts about the bank.
Liquidity tenor: Liquidity tenor: how long the bank's money is tied up by a product, the loan's maturity or a deposit's behavioural life. It sets the liquidity premium.
Interest tenor: Interest tenor: how long the product's rate is fixed for, until the next reset. It sets the base rate charged, not the liquidity premium.
Contingent liquidity charge: Contingent liquidity charge: the cost of the buffer a product makes the bank hold because it may need cash in a stress, such as an undrawn credit line.
Behavioural life: Behavioural life: how long a deposit with no fixed term actually stays, estimated from experience, as opposed to its contractual maturity of a day.
Base curve: Base curve: the risk-free curve FTP starts from, here the sterling overnight index swap (SONIA OIS) curve.
Continuous compounding: Continuous compounding: a rate r grows £1 to e^(rT) after T years; the equivalent annual rate is e^r − 1.

Deep Dives & Origins

Deep Dives

Financial Stability Institute, Liquidity transfer pricing: a guide to better practice, FSI Occasional Paper No 10, Bank for International Settlements, December 2011. Intermediate.
Committee of European Banking Supervisors, Guidelines on Liquidity Cost Benefit Allocation, October 2010. Intermediate.

Origins

Financial Stability Institute, Liquidity transfer pricing: a guide to better practice, FSI Occasional Paper No 10, BIS, 30 December 2011.
Committee of European Banking Supervisors, Guidelines on Liquidity Cost Benefit Allocation, 27 October 2010.
Basel Committee on Banking Supervision, Principles for Sound Liquidity Risk Management and Supervision, September 2008, Principle 4.

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