Presented by Meiting Liu The New Risk Management: The Good, the Bad, and the Ugly by Philip H. Dybvig, Pierre Jinghong Liang, and William J. Marshall Presented by Meiting Liu

Motivation At one time, risk management meant buying corporate insurance, implementing procedures to avoid lawsuits and accidents, and installing safety equipment. The new risk management uses financial markets to hedge different sources of risk within the firm. The new risk management can be good, bad and even ugly(Examples?). This article provides an introduction to the new risk management and some policy choices firms should be considering.

Outline Tools For The New Risk Management Four Fundamental Questions Option Pricing An example: Risk Management In Manufacturing Four Fundamental Questions Accounting Issues Cost Issues Risk Management Policy Conclusions

Background The Black- Scholes model 𝑐= 𝑒 −𝑞𝑇 𝑆 0 𝑁 𝑑 1 − 𝑒 −𝑟𝑇 𝐾𝑁 𝑑 2 𝑝= 𝑒 −𝑟𝑇 𝐾𝑁 −𝑑 2 − 𝑒 −𝑞𝑇 𝑆 0 𝑁 −𝑑 1 𝑑 1 = log 𝑆 0 𝐾 + 𝑟−𝑞+ 1 2 𝜎 2 Τ σ Τ , 𝑑 2 = 𝑑 1 −σ Τ An example of B-S extensions – Caplets: 𝑐𝑎𝑝𝑙𝑒𝑡𝑠(0, 𝑇 𝑖−1 , 𝑇 𝑖 ,𝐾, 𝑣 𝑖 )= 𝑃 0, 𝑇 𝑖 𝜏 𝑖 ( 𝐹 𝑖 0 𝑁 𝑑 1 (𝐾, 𝐹 𝑖 0 , 𝑣 𝑖 ) − 𝐾𝑁 𝑑 2 (𝐾, 𝐹 𝑖 0 , 𝑣 𝑖 ) ) 𝑑 1 = log 𝐹 𝐾 + 𝑣 2 𝑣 , 𝑑 2 = 𝑑 1 − 𝑣 2 𝑣 𝑖 2 = 𝑇 𝑖−1 𝑣 𝑇 𝑖−1 −𝑐𝑎𝑝𝑙𝑒𝑡𝑠 2 𝑣 𝑇 𝑖−1 −𝑐𝑎𝑝𝑙𝑒𝑡𝑠 2 = 1 𝑇 𝑖−1 0 𝑇 𝑖−1 𝜎 𝑖 (𝑡 ) 2 𝑑𝑡

Background Hedging Strategy An investment policy with an investment equal to the model’s option price and a terminal value equal to the terminal value of the option. To make an arbitrage profit if market prices are out of line with the model. If the model price of a Call is lower than the price in the economy: Selling Call + Buying Shares + Borrowing If the model price is higher than the price in the economy: Buying Call + Shorting Shares + Lending

An Example: Risk Management in Manufacturing Settings A manufacturer uses significant amounts of copper as an input The expected output is 1,000 units, which will sell for $100 per unit The price has been committed to in advance because of long-term contract The quantity may vary around this expectation. Each unit will use an amount of copper that would cost $20 purchased forward (in a firm commitment to buy one year from now). If purchased in the spot market, the copper in the unit might cost $25 (with probability 1/4), $20 (with probability 1/2), or $15 (with probability 1/4). Assumes no taxes and sources of risk that are not related to the price of copper.

Approach Panel A: Unhedged Cash Flows Prob Copper price ($) Units sold Output Total Sales ($) Copper Expense ($) Other Expense($) Profit (loss) ($) ¼ 25 1,200 100 120,000 30,000 82,000 8,000 ½ 20 1,000 100,000 20,000 78,000 2,000 15 800 80,000 12,000 74,000 (6,000) The expected unhedged profit = ¼ * 8000 + ½ * 2000 – ¼ * 6000 = 1500

Hedged Profit (loss) ($) Approach Panel B: Naive Hedge of the Expected Quantity Required Probability Unhedged ($) Hedged ($) Hedged Profit (loss) ($) ¼ 8,000 5,000 13,000 ½ 2,000 (6,000) (5,000) (11,000) The expected naïve hedged profit = ¼ * 13000 + ½ * 2000 – ¼ * 11000 = 1500

Hedged Profit (loss) ($) Approach Panel C: Fully Hedged Cash Flows Probability Unhedged ($) Hedged ($) Hedged Profit (loss) ($) ¼ 8,000 (6,500) 1,500 ½ 2,000 (500) (6,000) 7,500 How to realize that? By simply buying or selling forwards?

Approach: The Dynamic Hedge Why ? Assume that the firm is using copper futures contracts to hedge and the reinvestment rate is 5% over 6 months Assume information arrival and trading occur now, in six months, and again in a year Future Price Dynamics for the Copper Hedge Now 6 months 12 months $25 $20 $20 $15 ¼ ½ $22.5 ¼ ¼ ½ $17.5 ¼

The Dynamic Hedge Strategy: At the start, the firm sells 1,400/1.05 ≈ 1,333 futures at the futures price of $20. In 6 months, if the futures price goes up to $22.50, the short position will decrease to 1,200 contracts. If the futures price goes down to $17.5, the position will increase to 1,600 contracts. In 6 months, the futures price goes up to $22.50, the firm loses $3,333 on the short futures and borrows at the riskless rate, agreeing to pay back $3,333 * 1.05 = 3,500 in 1 year. To make sure a full hedge, the short position in 6 months reduces to Δloss/ Δprice= (6,500 – 3,500) / (25 – 22.5) = 1,200 contracts. In a year, the hedged cash flows = 1,500

Four Fundamental Questions Why Should We Hedge? What Risks Should We Hedge? With What Instruments Should We Hedge? Support Your Investment Banker

Question 1: Why Should We Hedge? Increase the firm value Reduces the volatility of the value received by shareholders? Reduce the bankruptcy cost and costs of financial distress The reduction of risk can maintain more leverage to reduce taxes and avoid double taxation Reduce earnings volatility Give managers incentives to produce profits

Question 2: What Risks Should We Hedge? suppose we are hedging a bank’s exposure to interest rate risk. Should we hedge: the direct interest mismatch of existing assets and liabilities? or the full economic value? If the purpose of hedging is to eliminate sources of noise beyond the manager’s control, it may even be appropriate to hedge particular accounting numbers used in computing compensation rather than hedging cash flow or economic value.

Question 3: With What Instruments Should We Hedge? To hedge U.S. interest rates Bonds, repurchase agreements, Treasury bond futures, swaps, caps, or collars. With which should we hedge? pricing transaction costs accounting implications

Accounting Issues Hedge accounting is a new and technical area The guide for hedge accounting standards SFAS No. 133: Accounting for Derivative Instruments and Hedging Activities Two hedge accounting methods: Fair value hedge: hedge the fluctuation of the fair value Cash flow hedge: hedge the fluctuation of the cash flow What method should we used in the manufacturing example? Cash flow hedge

Accounting Issues Several conditions must be met to qualify for cash flow hedge accounting treatment: The nature of the risk to be hedged The hedge must be deemed effective Formal and complete documentation of hedging activities The forecasted future transactions: single/similar Likelihood of the forecasted future transactions must be “probable” Question: Is the hedge in our example qualified for it? Interesting accounting challenge

Cost Issues Cost of hedging is the cost of any securities purchased in the hedge program. Transaction Cost Commissions Bid-ask spread Any internal costs of trading Marginal Cost Hedged price or Spot price? The price has been locked in for a fixed quantity The profit/loss will be collected on the hedged quantity regardless of how much or little is actually used. If more is needed, the shortfall will be purchased at the spot price. If less is needed, the excess will be sold at the spot price. Spot price!

Risk Management Policy Specify the goal and scope of any hedging activity Dictate the degree of centralization The control systems Ex post evaluation Monitor and limit the amount of risk taken

Conclusion Risk management in corporate policy Derivatives in risk management Implementing new accounting standards in risk management Internal controls and policies

Thoughts about the Paper Merits The framework of the paper is clear and complete The manufacturing hedging example is useful to understand the dynamic hedging and its advantage The conclusion is proved by the real-world firms Improvements Issues can be further updated: Financial technology, regulation and legislations The bias of the theory: B-S Formula

Further Reading Risk Management Information Hedging with Options Hedging Programs That Failed Value at Risk Hedge Accounting Sources