Project specific risks, catastrophic risks and the use of risk - - PowerPoint PPT Presentation

Project specific risks, catastrophic risks and the use of risk premiums

Mark Freeman

Accounting for the timing of costs and benefits in the evaluation of health projects relevant to LMICs 14th September 2017

Mark Freeman (University of York) Risk & Valuation September 2017 1 / 14

What is appropriate for valuing healthcare in LMICs?

Risk matters

Macroeconomic risk has a different valuation implication (precautionary saving) than project uncertainty (risk premium) Risk should not be measured by standard deviation alone. Higher moments matter Low probability, but potentially catastrophic, economic outcomes can significantly influence valuations Risk premiums can be negative, increasing healthcare project valuation National or international perspective?

Mark Freeman (University of York) Risk & Valuation September 2017 2 / 14

Risk-free or risk-adjusted discounting?

Risk-free discounting

Many governments value all social projects using the simple Ramsey rule (e.g. UK for horizons < 30 years). Based on the Arrow-Lind theorem

Risk-adjusted discounting

Others (e.g. French, Dutch and Norwegian), explicitly allow for risk in valuation, as project benefits generally relate to the overall macro-economy (non-zero ‘beta’).

Central ground

Some argue that risk premiums are too small to concern us. The US discounts at 7% and 3% (2.5%, 3% & 5% climate change, 3% health).

Mark Freeman (University of York) Risk & Valuation September 2017 3 / 14

Stylistic example

Binomial process for consumption

Current aggregate consumption c0 = $1, 000. Consumption in 10 years of cu (probability π) or cd (probability 1 − π).

Parameterizing

We set cu, cd and π so that future (10-year) consumption has an expectation of $1,200 with a standard deviation of $300. Vary π, let the mean and standard deviation determine cu and cd.

Mark Freeman (University of York) Risk & Valuation September 2017 4 / 14

The consumption process

500 1,000 1,500 2,000 2,500 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Future consumption Probability of being in the up state Consumption in the up state Consumption in the down state Low probability of severe consumption catastrophe

Mark Freeman (University of York) Risk & Valuation September 2017 5 / 14

An LMIC healthcare project

Another binomial process

Healthcare project with monetized benefit of bu or bd in ten years: Pro-cyclical: bu occurs iff cu occurs; probability π Counter-cyclical: bu occurs iff cd occurs; probability 1 − π Also look at risk-free and acyclical projects.

Parameterizing

bu and bd set so the expected benefit is $2, with standard deviation to $1. They depend on π.

Mark Freeman (University of York) Risk & Valuation September 2017 6 / 14

Cyclical benefits

• 1

1 2 3 4 5 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Benefit Probability of being in the up state benefit in up state (pro-cyclical) benefit in down state (pro-cyclical)

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Counter-cyclical benefits - Mirror image

• 1

1 2 3 4 5 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Benefit Probability of being in the up state benefit in up state (counter-cyclical) benefit in down state (counter-cyclical) Low probability of consumption catastrophe associated with high project benefits Mark Freeman (University of York) Risk & Valuation September 2017 8 / 14

Valuing the healthcare project

Equilibrium

Social planner gets time separable utility e−ρtU(ct) from aggregate

• consumption. In equilibrium, the present value, p, of the project:

U(c0 − p) + e−ρtE[U(ct + b)] = U(c0) + e−ρtE[U(ct)]

The utility function

Power utility with relative risk aversion = 2, rate of pure time preference ρ = 1%.

Mark Freeman (University of York) Risk & Valuation September 2017 9 / 14

Present value of the risk-free project

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Present value of the project Probability of being in the up state PV (risk-free) PV (risk-free, certain consumption) Precautionary effect increases price of risk-free projects (extended Ramsey Rule) Precautionary effect gets stronger with catastrophic consumption

• utcomes (Rietz 1988, Barro 2006 &

2009, Gabaix 2012) Mark Freeman (University of York) Risk & Valuation September 2017 10 / 14

Present value of the pro-cyclical & acyclical projects

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Present value of the project Probability of being in the up state PV (pro-cyclical) PV (independent) PV (risk-free) Positive (zero) risk premium for positive (zero) beta healthcare project (CCAPM) Risk premium high in the presence

• f catastrophic risk (Rietz, 1988;

Barro 2006 & 2009; Gabaix 2012) High sensitivity of valuation to precise likelihood and outcome of catastrophe (Martin, 2013; Gollier, 2016) Mark Freeman (University of York) Risk & Valuation September 2017 11 / 14

Present value of the counter-cyclical project

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Present value of the project Probability of being in the up state PV (counter-cyclical) PV (risk-free) Counter-cyclical projects more highly priced than risk-free assets (CCAPM) Projects with strong payoffs in catastrophic states are very highly valued (e.g. Weitzman 2007 & 2009, Dietz 2011, Barro 2013, Pindyck 2013). Discount rate here negative. Mark Freeman (University of York) Risk & Valuation September 2017 12 / 14

A counter-cyclical healthcare project

Healthcare projects in LMICs to protect against economic collapse

Consider an LMIC that, in the event of an economic collapse (low probability event), expects a healthcare crisis (famine, malaria outbreak, etc.).

Project to protect against this outcome

Since this project’s benefits are greatest in catastrophic states, it has very high value.

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What is the ‘beta’ of a healthcare project

National or international perspective

The probability of catastrophic economic outcomes, and the relationship with healthcare projects, within LMICs are greater/stronger on a national than international perspective. Proper international support would help mitigate national effects Therefore, when undertaking these valuations, an assessment needs to be made of the international policy response to a disaster

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