Reference: what the grader recomputes

A funding mark, a cash receipt and a capital allowance answer different questions. This reference sets out the calculations the grader uses to keep them separate; The funding option explains the commercial decision.

The formulas apply to the synthetic BOOK case under its published conventions. Amounts are USD unless labelled USD millions; spreads are annual decimals and one basis point, or bp, is 0.0001. Official rules supply selected prudential requirements. Quotes, default models, settlement conventions and the capital price remain disclosed case assumptions.

Symbols and scope

1. A quote-supported funding value

The economic specification sets USD1bn notional, twenty-year funding and a five-year deployment. Its pricing grid uses $q=0.25$ and nominal OIS $r=0.04$, compounded quarterly. OIS is the overnight-indexed swap benchmark. Actual dated payments retain their contractual day counts.

Discounting puts payments on a common valuation date; the annuity prices a unit annual spread:

$$d_r(t)=(1+rq)^{-t/q}, \qquad A_r(h)=\sum_{j=1}^{h/q}q\,d_r(jq) =\frac{1-d_r(h)}{r}.$$

A replacement quote must match the surviving contract's reference, quantity, notional, maturity, payment terms and legal rights. The financing advantage is the difference between matching replacement and locked spreads, multiplied by the annuity:

$$F=N(m-k)A_{\mathrm{quote}}(h), \qquad \mathrm{DV01}_{F}=NA_{\mathrm{quote}}(h)\,10^{-4}.$$

The preserved formula calls the positive sensitivity $\mathrm{DV01}_F$. In prose we call it widening gain per bp, to distinguish it from negative desk duration. The opening internal spread is 20bp plus a 50bp locked increment, giving 70bp financing against a 100bp replacement quote.

Full legal value also includes the unsettled reference return and identified stub items:

$$\begin{aligned} J_{\mathrm{ref}}(t) &=d(t,t_{\mathrm{next}})N\bigl(p_U(t)-p_{\mathrm{last}}\bigr),\\ V_{\mathrm{legal}}(t) &=F(t)+J_{\mathrm{ref}}(t)+U_{\mathrm{stub}}(t). \end{aligned}$$

Here $p_U$ is the normalised note price and $p_{\mathrm{last}}$ its last settled reset price. The adjustment is added once to a quote reset to today's reference basis. An original-basis quote may already include it. An unknown stub cannot silently become zero.

The reference note is repriced using its fixed 5% coupon $c_U$ and the selected credit-yield shock $x_U$:

$$p_U(h,x_U)=c_UA_{c_U+x_U}(h)+d_{c_U+x_U}(h).$$

This is a yield snapshot. A floating-rate scenario needs its own coupon resets and discounting. The direction convention is

$$\mathrm{P\&L01}_s=\frac{\partial V}{\partial s}\,10^{-4}, \qquad \mathrm{DV01}_{\mathrm{desk},s}=-\mathrm{P\&L01}_s.$$

The twenty-year/five-year comparison and its numerical table live in The funding option. A funding allocation is a management comparison, rather than another loan asset or cash expense.

2. Return settlement and the source of principal

The provider owns U and receives its distributions; Meridian receives the contractual total return swap (TRS) remittance. With distribution $d_j$ per unit of face and settlement fraction $\Delta t_j$, the net receipt is

$$\mathrm{TRS}_{j} =N\bigl(d_j+p_j-p_{\mathrm{last}}\bigr) -N\Delta t_j\bigl(\mathrm{OIS}_j+k\bigr).$$

At redemption the ex-distribution price is zero and the distribution contains principal. Adding another principal receipt would count it twice. The original sale supplies cash; the unfunded derivative supplies no second advance.

The case's accounting opinion retains U and a financing liability, citing IFRS 9 paragraphs 3.2.15, B3.2.14 and B3.2.16(o). This is a case assumption. Its paragraph 3.2.22 citation addresses unsupported offsetting. Regulatory classification is selected separately by the fictional classification letter.

3. Default loss is not a supplied exposure path

Credit valuation adjustment (CVA) prices expected loss if the provider defaults while owing a positive close-out amount. The flat-hazard case model derives default intensity and survival from provider CDS spread $s_P$ and recovery $R_P$:

$$\lambda_P=\frac{s_P}{1-R_P}, \qquad S_P(t)=e^{-\lambda_Pt}.$$

Credit default swaps (CDS) cover specified default events. The selected model places default after quarterly payment and sums discounted loss over that grid:

$$\mathrm{CVA} =\sum_j d_{\mathrm{OIS}}(t_j)(1-R_P) \bigl[S_P(t_{j-1})-S_P(t_j)\bigr] \mathbb{E}\!\left[E_j^+\mid P\text{ defaults at }t_j\right].$$

The conditional positive exposure $E_j^+$ must be repriced from the contract, reset state and collateral recovery. It is not supplied as an answer vector. Before return settlement, the reference-price adjustment can materially change the amount owed.

The provider's CDS prices provider default. The desk's own borrowing spread prices cash debt. Its base bond spread is 50bp and own CDS 30bp; their 20bp basis cannot replace the full borrowing premium unless the comparison already charges the credit component.

4. A reserve expense does not borrow cash

A reserve expense can reduce equity without a payment. Actual borrowing instead begins with accessible cash after contractual receipts, payments and existing debt interest. For executed available capacity $L_{\mathrm{avail}}$:

$$\begin{aligned} C_{\mathrm{pre}} &=C_{\mathrm{open}}+\mathrm{receipts}-\mathrm{payments},\\ B_{\mathrm{need}}&=\max(0,-C_{\mathrm{pre}}),\\ B_{\mathrm{draw}}&=\min(B_{\mathrm{need}},L_{\mathrm{avail}}),\\ \mathrm{shortfall}&=B_{\mathrm{need}}-B_{\mathrm{draw}}. \end{aligned}$$

A draw creates cash and debt together. A funding-mark rise with no cash deficit creates neither. By contrast, a settled reference-price loss can create a deficit and later interest on the resulting draw. Cash sweeps and repayments follow their own terms.

The conditional quadratic experiment

The separate prefunding experiment actually borrows and deposits funds externally at OIS. It has its own USD100m buffer and assumes an own-spread response of 50bp plus the same nonnegative funding move $x$. Beginning-quarter deposits and end-quarter interest give

$$\begin{aligned} L_j(x)&=NxA_r\bigl(20-(j-1)q\bigr),\\ I&=N\sum_{j=1}^{80}q\,d_r(jq)A_r\bigl(20-(j-1)q\bigr),\\ \mathrm{UFVA}_{\mathrm{conditional}}(x)&=Ix(0.005+x). \end{aligned}$$

Both the deposit and its spread cost rise with $x$, creating the quadratic term. This follows from the specified transaction, not a rule that valuation reserves create debt. The historical quarter-grid result at 100bp is about USD17.958836m. The separately recorded rough estimate uses different inputs:

$$\mathrm{USD}\,70\mathrm{m}\times0.015\times13.8 =\mathrm{USD}\,14.49\mathrm{m}.$$

Released deposit principal repays matched debt; the buffer pays interest. Reserve consumption records the expense separately and cannot become another cash source. Received variation margin (VM) reduces a funding need only after settlement and only where its use is permitted. The prefunding experiment fixes reusable VM at zero.

5. Classify the contract before measuring exposure

The fictional classification annex selects the standardised approach for counterparty credit risk (SA-CCR). Basel CRE52 supplies the exposure rules for an enforceable netting set: contracts whose amounts may be offset on close-out.

Replacement cost $RC$ uses legal value $V$, recognised collateral $C$, threshold $TH$, minimum transfer amount $MTA$ and net independent collateral $NICA$. Subscripts distinguish unmargined and margined treatment:

$$\begin{aligned} RC_u&=\max(V-C,0),\\ RC_m&=\max(V-C,TH+MTA-NICA,0). \end{aligned}$$

Received collateral is positive and posted collateral negative. U held by the provider is not collateral received by Meridian against that provider's default.

Potential future exposure $PFE$ adds protection against changes before close-out. Here $A$ is the supervisory add-on:

$$\mu=\min\left(1,0.05+0.95\exp\!\left[\frac{V-C}{2(0.95)A}\right]\right), \qquad PFE=\mu A.$$

At zero add-on, PFE is zero without division. At exact collateral coverage with a positive add-on, the multiplier is one. Exposure at default combines replacement cost and PFE, with the margined cap calculated against the same set:

$$EAD_u=1.4(RC_u+PFE_u), \qquad EAD_m=\min\bigl(1.4(RC_m+PFE_m),EAD_u^{\mathrm{same\ set}}\bigr).$$

Supervisory duration $SD$, maturity factor $MF$ and supervisory delta $\delta_{\mathrm{sup}}$ determine effective notional. $S$ and $E$ are reference start and end times, $M$ derivative maturity, and $b_{10}$ ten business days under the selected conversion. MPOR is the margin period of risk:

$$\begin{aligned} SD&=\max\left(\frac{e^{-0.05S}-e^{-0.05E}}{0.05},b_{10}\right),\\ MF_u&=\sqrt{\frac{\min(\max(M,b_{10}),1\ \mathrm{year})}{1\ \mathrm{year}}},\\ MF_m&=1.5\sqrt{\frac{MPOR}{1\ \mathrm{year}}},\\ D_{\mathrm{eff}}&=N\,SD\,MF\,\delta_{\mathrm{sup}}. \end{aligned}$$

The supervisory 5% decay differs from 4% OIS. The case uses twenty-business-day MPOR and 250 business days per year, giving a margined factor about 0.424264. Daily exchange alone cannot justify the shorter counterexample period.

For one reference entity, the credit add-on is

$$\mathrm{AddOn}_{\mathrm{credit}} =\left|SF\,D_{\mathrm{eff}}\right|.$$

The selected AAA supervisory factor $SF$ is 0.38%; the return receiver's credit delta is minus one. Reference-credit risk and the provider's counterparty risk weight remain different inputs.

6. Eligibility comes before a collateral haircut

CRE22 requires applicable rights and eligibility before recognising collateral. Counterparty-issued or related securities fail the selected gate. In the stated ratings-permitted branch, ordinary sovereign debt below BB- and non-sovereign debt below BBB- fail the respective thresholds.

For exposure $E$, collateral $C$ and exposure, collateral and currency haircuts $H_e$, $H_c$, $H_{fx}$, the comprehensive approach gives

$$E^*=\max\bigl(0,E(1+H_e)-C(1-H_c-H_{fx})\bigr), \qquad RWA=E^*RW_{\mathrm{counterparty}}.$$

Risk-weighted assets (RWA) apply the counterparty weight to adjusted exposure. Direction matters: when Meridian borrows against securities, the securities posted are its exposure and cash received is its collateral against the lender.

The supervisory haircut scales with revaluation interval $N_R$ and minimum holding period $T_M$:

$$H=H_{10}\sqrt{\frac{N_R+T_M-1}{10}}.$$

The lender's commercial haircut instead determines cash advanced. The allocation calculation needs both. A rating change requires dated evidence; a spread move alone cannot establish an eligibility cliff.

7. Recognition cannot extend a hedge's contract

After provider, coverage, currency and enforceability tests, CRE22 adjusts otherwise eligible protection $P$ for maturity mismatch:

$$\begin{aligned} T&=\min(5,\text{exposure residual years}),\\ t&=\min(T,\text{protection residual years}),\\ P_a&=P\frac{t-0.25}{T-0.25}. \end{aligned}$$

Recognition also requires at least one year of original protection maturity and three months remaining when a mismatch exists. The immediate twenty-year/five-year comparator has an initial factor of one because $T$ is capped at five. It still leaves fifteen years uncovered.

The quoted action begins at model year 0.008 and expires at 5.008, leaving 14.992 years plus its initial delay. LEV30 separately addresses purchased protection used to offset written-credit leverage exposure; that test has no five-year cap.

One book, different end dates

The loan repays at year 5.00. The funding contract continues to year 20.00. Getting the principal back does not end the bank's obligations to the funding provider.

Years after book inception. Every strip uses the same proportional time scale.

05101520

Funding contract0 to 20.00 years

Loan investment0 to 5.00 years

Filled, the original loan. Outline, principal reinvested for the remaining 15.00 years at the overnight indexed swap benchmark, or OIS. The old loan margin does not continue.

A separate protection option

The quoted credit default swap, or CDS, protects against the specified funding-provider default. This controlled comparison is not a hedge executed in the base book.

Contractual protection0.008 to 5.01 years

Hatching marks 14.99 years without this protection after expiry. No renewal is assumed. The initial 0.008-year delay is too short to distinguish at this scale.

The capital calculation caps exposure maturity at 5.00 years. Its initial maturity factor is 1.00, meaning full maturity recognition for the quoted protection amount. That regulatory treatment cannot extend the contract.

Controlled CDS option. Recognition is for counterparty credit risk, not a measure of whole-book risk removed.

Source snapshot	Book year	Protection left, years	Maturity factor
Protection begins	0.01	5.00	1.00
Maturity recognition stops	4.76	0.25	0.00
Contractual protection expires	5.01	0.00	0.00

The table scrolls horizontally on narrow screens. At year 4.76, maturity recognition is zero even though contractual protection lasts another 0.25 years.

Why the simple example says 15.00 years

The immediate-execution comparator starts 5.00-year protection at book inception. That leaves 15.00 years after expiry. The quoted action shown here starts at model year 0.008 and expires at 5.01, leaving 14.99 years. The comparator and the quoted action use different clocks.

8. CVA capital and the price of capital

CVA adjusts value for expected loss. CVA capital addresses changes in that adjustment. The case selects the reduced basic approach under MAR50. Netting-set maturity $M_{NS}$, exposure and counterparty CVA risk weight $RW_c$ feed the aggregation:

$$\begin{aligned} DF_{NS}&=\frac{1-e^{-0.05M_{NS}}}{0.05M_{NS}},\\ SCVA_c&=\frac{RW_c}{1.4}\sum_{NS\text{ of }c}M_{NS}EAD_{NS}DF_{NS},\\ K_{\mathrm{CVA}}&=0.65\sqrt{\left(0.50\sum_c SCVA_c\right)^2 +0.75\sum_c SCVA_c^2}. \end{aligned}$$

The maturity has no five-year cap here, and the 0.65 scalar applies once. A recognised hedge can add its own provider exposure; default protection and CVA hedge recognition require separate checks.

Whole-book leverage includes applicable assets and exposures under LEV30. The selected capital convention uses available Tier 1 capital and a 3% minimum:

$$\mathrm{leverage\ ratio}=\frac{\mathrm{Tier1}_{\mathrm{available}}}{L_{\mathrm{book}}}, \qquad \mathrm{minimum\ Tier1}=0.03L_{\mathrm{book}}.$$

The desk's all-equity allocation takes the larger selected risk-based and leverage requirement:

$$K_{\mathrm{desk}}(t) =\max\bigl(0.08RWA_{\mathrm{book}}(t),0.03L_{\mathrm{book}}(t)\bigr).$$

The 8% total-capital minimum is from RBC20. Taking this maximum as equity is a desk convention. Capital valuation adjustment (KVA) prices incremental capital on the same opening portfolio with and without the action, using a 10% hurdle:

$$\mathrm{KVA}_{\mathrm{incremental}} =0.10\sum_j q\,d_{\mathrm{OIS}}(t_j) \mathbb{E}\!\left[K_{\mathrm{with}}(t_{j-1}) -K_{\mathrm{without}}(t_{j-1})\right].$$

Capital is sampled at the beginning of each interval and charged at its end. Expectations need disclosed scenario weights or a deterministic path. Capital headroom can improve capacity without becoming spendable cash.

9. Two management pots and one journal

The management ledger separates clean funding gain $G$, hedge value $H$, positive deferral $D$ and reserve deduction $X$. With cash $C$, other nonoverlapping assets $M$ and liabilities $B$:

$$E_{\mathrm{management}}=C+M+G+H-B-D-X.$$

Component cash flows, valuation changes, funding expense $f$ and other expense $o$ explain P&L:

$$\mathrm{P\&L} =CF_G+\Delta G+CF_H+\Delta H-f-o-\Delta D-\Delta X.$$

Borrowing principal, returnable margin and capital issuance change stocks without becoming trading income. Whole-book attribution adds the separately recorded deployment, reference and legacy-debt results.

Rolling opening inputs, repricing markets and applying effective actions in that order attributes each deduction $R$:

$$\begin{aligned} \theta_R&=R_{\mathrm{open}}-R_{\mathrm{roll}},\\ \mathrm{market}_R&=R_{\mathrm{roll}}-R_{\mathrm{preaction}},\\ \mathrm{action}_R&=R_{\mathrm{preaction}}-R_{\mathrm{close}}. \end{aligned}$$

Expected reserve release is already inside the closing reserve movement. Adding it again invents profit. The original funding deferral follows its frozen 30bp schedule:

$$D(t)=N(0.003)A_r(20-t).$$

Risk adjustments are remeasured separately. For a separately recognised instrument, the case's accounting opinion applies IFRS 9 paragraphs 5.1.1A and B5.1.2A to unsupported day-one differences. This case assumption concerns the actual unit, not overlapping gross rights.

Independent journals reconstruct closing assets, liabilities and equity. The unresolved USD500,000 claim and allowance survive contractual maturity until their own payment or write-off event.

10. Prudent valuation concerns uncertainty, not reserve size

The separate EU-style annex applies to an identified recognised fair-valued unit. Its synthetic cost distribution determines expected exit cost $c_x$, same-source prudence $u_x$ and prudent percentile cost $q_{0.90,x}$ against base value $B_x$. $FV_x$ is accounting fair value and $PV_x$ prudent value:

$$\begin{aligned} FV_x&=B_x-c_x-u_x,\\ PV_x&=B_x-q_{0.90,x},\\ FV_x-PV_x&=q_{0.90,x}-c_x-u_x. \end{aligned}$$

The prudent-valuation RTS supplies the 90% criterion. It concerns plausible current exit values, not a fraction of the reserve. Selected Method 1 aggregates positive residual adjustments as

$$APVA_x=(1-0.50)(FV_x-PV_x), \qquad AVA_{\mathrm{model}}=\sum_x APVA_x.$$

The amended Annex supplies the 50% aggregation factor. The temporary 66% factor expired; negative deductions and repeated offsets are excluded. For this increment, CRR Article 34 gives the common equity Tier 1 (CET1) bridge:

$$CET1_{\mathrm{after}}=CET1_{\mathrm{before}}-AVA_{\mathrm{increment}}.$$

A smaller deduction restores headroom. It does not supply cash or trading income. Other prudent-valuation categories remain outside this controlled example rather than being assumed absent for the bank.

11. Allocation prices both haircut systems

For indivisible lot value $V_i$ assigned to lender $l$, commercial haircut $h_l^{\mathrm{market}}$ determines cash. Supervisory haircut $H_i$ and lender weight $RW_l$ determine selected capital:

$$\begin{aligned} C_{il}&=V_i(1-h_l^{\mathrm{market}}),\\ E^*_{il}&=\max\bigl(0,V_i(1+H_i)-C_{il}\bigr),\\ K_{il}&=0.08RW_lE^*_{il}. \end{aligned}$$

The allocation convention prices lender spread $s_l$, own funding premium $f$ and equity cost over seven days for binary assignment $x_{il}$:

$$J(x)=\frac{7}{365}\sum_{i,l}x_{il} \left[C_{il}s_l+(V_i-C_{il})f+0.10K_{il}\right].$$

Each lot is assigned once, subject to at least USD230m external cash, no more than USD2m incremental capital, issuer concentration, rights and capacity. Common OIS cost is constant across these assignments; actual interest still enters settlement.

The optimum assigns both large lots to Tol and all 50 small lots to Div. Assigning 49 small lots to Div costs about USD50.49 more over seven days. The final transfer raises capital but reduces total cost, illustrating why either haircut system alone gives an incomplete objective.

W3 from a mark to the graded report

W3 observes the first quarterly TRS settlement under joint shocks. The case exhibits specify OIS at 4%, funding spread widening and a reference-credit move from 100bp to 350bp. Start by repricing U at its actual remaining 19.75-year term, then compute its return from the last settled price. Add the matching funding component and any stated stub to obtain full legal value.

Next, apply the payment sequence: U's coupon enters once through the TRS; contracted financing is paid; the loan pays its locked coupon; legacy interest is paid. Only the remaining cash deficit drives a facility draw. The loan has 4.75 years left and is marked against its own shocked curve. That mark loss is noncash unless its contract requires settlement.

Then compute provider loss exposure, regulatory exposure and capital under their own curves and rules. Reconcile settlement, debt and reserve movements through the journal. These feed the financial owners: contract and mark, credit and cash funding, capital and protection, capacity, liquidity, recognition and reconciliation. Institutional owners separately require supported rights, authority, client outcome and recommendation.

This is a calculation walkthrough, not a new scored W3 run. Each panel keeps its specified scenario and clock; controlled comparisons cannot be combined into one actual book.

Daily-period calculation

How the book is scored defines the elapsed-day-weighted owner sum. Missing days stay in the configured denominator, later repairs do not erase earlier checkpoints, and fatal violations remain separate from points. A no-action run has no score; an accepted hold is an explicit decision.

The observation grid must also stay separate from contractual payments. More display points cannot create another coupon or another capital-charge interval. The limitations page records the executed checks and unexercised dimensions.

Dated source register

We use the case's accounting opinion for recognition assumptions, CRE22 for collateral and maturity recognition, CRE52 for counterparty exposure, MAR50 for CVA capital, LEV30 for leverage exposure and RBC20 for minimum risk-based capital. The case specifies applicability; citing a chapter cannot establish fictional facts.

Quote conversion, settlement, reserve and capital-price conventions are documented in the economic specification, reserve module, capital rulebook, valuation-capital annex and allocation specification. Their disclosed choices are part of the task inputs.