XVA 4 - KVA: What happened to KVA?
KVA (Capital Valuation Adjustment) has been discussed for many years but has never really entered the ‘real world’ pricing used by banks.
In theory, KVA is a very useful calculation and could be used to manage the capital use of derivatives in much the same way CVA and FVA are routinely hedged and managed. But why is KVA not included?
Most market practitioners point to the calculation methodology (see below) and the difficulty of actually hedging the components when they are not traded and/or have transparent markets inputs.
But there is another explanation: KVA is often a very large cost input to a derivative price and can make the bank uncompetitive with their clients. The more favoured approach is to use RoC or RoE (Return on capital or equity) measures which are more reflective of the way a bank looks at capital returns and, conveniently tend to be lower cost!
Despite KVA not being used regularly, many banks still calculate KVA for deals and portfolios as a ‘baseline’ capital return even if they do not include this in pricing.
The KVA formula
The calculation of KVA is actually quite simple for a single trade:
KVA = ∑ (EC * CC * ti)
EC is the discounted expected capital profile
CC is the bank cost of capital (usually in percent)
ti is the ith time period
This is all very straight forward except:
The capital calculation is very bank and jurisdiction specific. While many jurisdictions are quite similar in their approach, some differences can occur. Also, there is a mix of standard and internal models across banks which adds to the complexity and difficulty of comparing KVA.
The EC includes SA-CCR (credit) and market risk (Basel II and III) capital. These calculations often incorporate many products with specific add-ons which can be computationally complex.
Portfolio effects can be quite complex when using standard models to calculate the EC. So, adding a new trade to the portfolio is not straight forward and requires a knowledge of a large number of trades and products to accurately calculate the EC.
How does KVA differ from CVA and FVA?
CVA and FVA are routinely booked to P&L for banks. The P&L changes with market inputs which are readily available (e.g., interest and FX rates) or sourced internally (FTP - funding transfer pricing which is the cost of funding over a base curve).
CVA and FVA are commonly hedged by XVA desks to minimise P&L fluctuations and ensure the performance of the business.
KVA is rarely (if ever) taken to P&L. It is associated with a return on capital and is closely related to RoC and RoE. The inherent challenges of calculating KVA and possibly hedging KVA means most banks prefer to use the RoC and RoE measures to assess the returns rather than formally book the returns in the P&L. This is the major difference to CVA and FVA which are regarded as P&L adjustments rather than return hurdles.
Implications for the buy-side
While KVA is not regularly included in derivative pricing by banks, the alternatives of RoC and/or RoE are used.
In all cases, the calculations are for a return metric and are not booked as P&L items (i.e., reserved). Rather the additional spread is booked to P&L with no offsetting entry on the XVA desk.
The buy-side clients of the banks should be aware that:
Banks may not disclose KVA pricing, but many use the calculation (per trade) as the comparison with RoC and RoE.
I always price KVA because it is a very good indicator of capital returns and is bank independent. This allows for an easier comparison of bank charges for capital use and return.
It is always worth asking banks for a XVA breakdown including KVA. This will really help in understanding all the inputs to the final price.
Many banks are quite transparent in their disclosure of XVAs used in pricing derivations. This is becoming a more standard practice but is not universal.
I always calculate the XVAs per bank before requesting pricing. This helps identify potential problems with details of the trades (as they are communicated to banks) and these can be corrected early in the pricing process.
The XVAs are a very good way to compare banks and calculating the expected XVAs is essential in this comparison and the selection of winning bids in competitive tenders.
Summary
While KVA may not be a direct input to pricing of derivatives, it is still a very useful calculation for banks and buy side clients.
I always calculate the KVA per bank to compare with their ‘return’ spreads. This helps standardise the comparison across banks and helps clients identify possible issues in the pricing and therefore select winning bids in competitive tenders.
In my experience, KVA is a very useful metric and should be calculated.