*In an effort to better remember the papers I read, I'm starting a new section about my blog devoted to short summaries of papers I find interesting. It's called "Analytics Corner". *

**Citation:** Arnd Huchzermeier, Christoph H. Loch, (2001) Project Management Under Risk: Using the Real Options Approach to Evaluate Flexibility in R&D. *Management Science* 47(1):85-101. Link

**Summary: **The authors consider a situation where a manager developing a new product can either abandon, continue or improve the product during development. Theyanalyze the setting using dynamic programming, study the impact of five types of uncertainty on the real options value and obtain results counterintuitive to prevailing knowledge in option pricing theory, due to the unique features of the R&D real options framework. This paper contributes to improved risk management in R&D projects.

**Outline:**

1. Introduction and Literature Overview

2. Five types of operational uncertainty

Market payoff variability, (R&D) budget variability, performance variability, market requirement variability, schedule variability (project may finish ahead of or behind schedule.

3. The basic model

3.1 Contingent claims analysis

Motivation of the use of dynamic programming, justification of discounting at the risk-free rate.

3.2 A dynamic programming model of an R&D project

T discrete stages corresponding to regular design reviews, leading to market introduction. Market success is determined by product performance, modeled by a one-dimensional parameter i. Performance uncertainty is captured in the variability of a probability distribution, measured by higher variance given same mean. This causes product (expected final) performance to drift between review period. Hence the authors define transition probabilities from expected performance state i to expected performance stage j.

Performance may unexpectedly improve with probability p or deteriorate with probability 1-p. Improvement or deterioration are spread equally over the next N states. For instance the probability of improvement is p/N for j=i+1/2, i+1, ..., i+N/2. The parameters N and p can be chosen to approximate a distribution using its first two moments. At each time period, the manager can decide to abandon, continue or improve the project. (The originality of the paper comes from having the possibility to improve.) Improvement results of a mean shift of the transition probabilities by 1 (the index of each state j is increased by 1, both for improvement and deterioration.)

Expected payoff if the product is launched in state i is given by m+F(i)*(M-m) where m is the smaller margin if the project misses the performance level and competes only on cost and M is the profit margin if the project exceeds this performance level, and F(i) is the probability that performance i exceeds the market requirement D. This payoff function of i is assumed convex-concave increasing.

The authors then formulate the manager's problem as a dynamic programming problem, writing out Bellman's equations from T back to time 0, evaluating the value of three actions (abandon, continue and improve) at each time period. They characterize the optimal policy as follows, assuming the payoff function is convex-concave increasing: **there exists three functions L_u(t)>=L_m(t) and L_d(t) such that it is optimal to abandon if i<=L_d(t), and if i>L_d(t): continue if i>L_u(t) or i<=L_m(t) and improve if L_m(t)<i<=L_u(t). This is presented visually in Figure 4.**

4. Uncertainty and the Value of Flexibility

This section studies the impact of increasing the variance of certain key drivers, to see whether the intuition that higher uncertainty in project payoff increases the real option value extends to other types of uncertainty faced by R&D managers.

4.1 Market payoff variability

4.2 Budget variability

4.3 Performance variability

4.4 Market requirements variability

4.5 Schedule variability

5. Conclusion

**Why I like this paper:** I like the use of dynamic programming in a managerial context (this is one of the papers I gave to read to the doctoral students in my PhD course on nonlinear programming) and the visual nature of the optimal policy shown in Figure 4.

**Further Reading: **Real options: Managerial flexibility and strategy in resource allocation by Lenos Trigeorgis (1996)

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