A recent body of work extends the replicating portfolio approach to provide insights into valuation and measurement of key assets and entities of interest. In this post, I discuss some innovative examples that are worth noting.

Motivation

Here are some common problems in finance research:

• Valuation: “I want to value some asset X, but it’s not traded and has irregular cash flows, which is a problem. How can I go about doing this?”
• Risk Exposures: “I want to measure the risk exposures of some entity Y, but the task is complicated due to accounting issues.”
• Clean Measurement: “I want a clean measure of Z that is not tainted by issues like liquidity.”

Recent series of papers tackle these questions using an old idea embedded in option pricing: the replicating portfolio approach. Below I discuss some useful examples.

Cash Flows of Private Equity

Gupta and Van Nieuwerburgh (2021) estimate the risk-adjusted profits of private equity (PE) by netting out the returns of a replicating portfolio. Risk-adjusting for PE is very difficult given the irregularity of the observed cash flows and relative lack of transparency. The “standard” methods in the industry either do not adjust for risk (e.g. IRR) or only consider aggregate stock market risk.

Their innovation here is to construct a replicating portfolio that embodies the risk inherent in the cash flows of a PE investment.

To do so, they first estimate the exposure of PE funds’ cash-flows to the cash-flows of a set of publicly listed securities including stocks, REITs, infrastructure stocks, and natural resource stocks. This is essentially amounts to the loadings on the “basis assets” of the replicating portfolio. They then use an asset pricing model to price the time-series and the cross-section of zero-coupon bonds and equity strips. Together with the earlier result, they are able to compute the price of the replicating portfolio.

Synthetic Banks

Begenau, Schneider, and Piazzesi (2020) combine position data with price data to create a synthetic bank and measure its exposure to interest rate and credit risk.

The key idea is to capture a given bank’s balance sheet in terms of exposures to interest rate risk and credit risk. To do so, they first use regressions to measure factor exposures for many fixed income instruments. (Note that this step is actually not reliant on the bank position data.)

Then the bank-level regulatory data is used to derive position exposures. For example, if JPMorgan reports a securities position worth 14 percent of total assets, then it responds to realizations of interest rate and credit risk factors exactly like interest rate and credit risk factor portfolios worth 9 percent and 1 percent of assets, respectively.

A key assumption throughout this exercise is that the non-fixed income part of the bank operations is orthogonal to interest rate and credit risk. This is likely cash, which mitigates the associated concern.

Convenience Yields

A body of work looks at measuring the convenience yields associated with certain types of securities. Here the standard approach is to replicate the cash flows of the security and examine the differences in valuation.

For example, Du, Im, and Shreger (2018) measure the convenience yield of U.S. Treasuries as the difference between the U.S. Treasury dollar yield and the FX swap-implied dollar yield paid by foreign governments.

A more recent example is given by Mota (2021), who measure the safety premium in corporate bonds. Here the synthetic asset being created is a portfolio that combines the corporate bond and the maturity-matched credit default swap (CDS). The key assumption therefore is that the CDS perfectly hedges credit risk, in which case the cash flows are perfectly identical across the two assets.

Pseudo Firms

Culp, Nozawa, and Veronesi (2018) provide a slight variant of the approach which is also related to Mota (2021). They are not replicating any particular firm per se; instead, they create a hypothetical firm from which they can compute the credit spread.

Specifically, they consider a pseudo firm, whose assets are real-traded securities and liabilities are equity and zero-coupon bonds. This exercise allows the authors to then construct “pseudo corporate bonds” using options data and subsequently measure the “pseudo spreads.”

Their methodology is based on the old insight that corporate debt is economically equivalent to safe debt minus a put option on the firm’s assets. It is useful because it bypasses the issues one would encounter in looking at the actual credit spreads of a given company: liquidity in bond markets, covenants, search frictions, and impact of regulations.

As an example, consider the pseudo firm whose assets are the Amazon stocks, and the liabilities are equity and zero coupon debt (bonds) with some face value \(K\) and \(T\).

• It is important to note that there is no relation between the bonds issued by this pseudo firm and the actual bonds issued by Amazon. After all, the assets are completely different.

The holders of this pseudo firm’s corporate bonds receive \(\min(K, A_T)\), which is equivalent to the payoff of the zero-coupon debt \(K\) minus the payoff on a put option on Amazon. Since one observes the market price of treasuries and equity put options, we can thus compute observed market values of the pseudo corporate bonds.