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Introduction to Risk Management. Risk Management Prof. Ali Nejadmalayeri, a.k.a. “ Dr N ”. Origin of Risk Management. Mankind has always fear forces of nature and attempted to be in their “good” side

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introduction to risk management

Introduction to Risk Management

Risk Management

Prof. Ali Nejadmalayeri,

a.k.a. “Dr N”

origin of risk management
Origin of Risk Management
  • Mankind has always fear forces of nature and attempted to be in their “good” side
    • Natural deities sun, moon, water, etc. were thought of controlling entities of these forces
  • As man evolved, so did his methods of harnessing and controlling nature
    • Probability and statistics invented to deal with gambling and actuarial challenges
  • Modern financial theories and instruments are latest inventions to deal with risk!
    • Must read: Against the Gods: The Remarkable Story of Risk By Peter L. Bernstein
basic concepts
Basic Concepts
  • Imagine you want to make a car noise-free. What would you do?
    • Find out what “the noise” looks like
    • Design a wave with exact shape but opposite cycles to cancel the noise
    • Walla! You have a noise-free car!
  • Now imagine fluctuations in wealth, cash flows, values, prices, etc. How can you make them less volatile? Any ideas?
heuristically speaking
Heuristically Speaking

Imagine the fluctuations in value looks like this

Original Wave

heuristically speaking1
Heuristically Speaking

Original Wave

Now imagine that is financial instrument which its fluctuations in value looks like this, so if we add this instrument to the mix

Canceling Wave

heuristically speaking2
Heuristically Speaking

Resulting Wave

Original Wave

Then the resulting fluctuations should be a average of the two, much less volatile

Canceling Wave

risk management 101
Risk Management 101
  • Indentify the nature of risk
    • Price risk or quantity risk
  • For quantity risk, design insurance
  • For price risk, represent risk using:
    • Fluctuations of value, cash flows, etc.
    • Payoff of contractual agreements
  • Indentify the building blocks
    • Replicate the payoffs and fluctuations using other financial instruments
    • Construct a derivative with payoff replica
quantity risk
Quantity Risk
  • Early insurance companies like Lloyds of London wanted to offer a solution to an age-old problem:
    • If my shipments got lost in the high seas, how can my shipping business still survive?
      • Without insurance, pretty much no way!
  • Insurance, however, guarantees compensation of replacement cost for goods lost; solving quantity risk
price risk
Price Risk
  • Even if you still own 100% of goods, there’s no guarantee that value of these goods would stay same over time
    • Unless someone or something pays for losses of value due to natural fluctuation, you ought to live with risk
      • What if someone is willing to offer an “offsetting” payoff, maybe because they disagree with you on what is most likely next price movement?
      • Imagine you’re corn farmer and fear price of corn may drop drastically by the harvest time. What if another person thinks it would actually go up by then? You could strike a deal to sell him the corn!
forward futures
Forward & Futures
  • In ancient India and Mesopotamia, farmers presold their crop for a price to speculators and merchants who were willing to take risk. These are known as forward contracts.
  • In late 18th century, Chicago merchants offered “standardized” forward contracts for agricultural products. These are futures.
    • Today there multiple futures markets around the globe. To name a few, CME, CBOT, ICE, NYMEX, etc. Offerings ranges from wheat and corn to T-bills and Fed Fund to Weather!
futures
Futures
  • Contract to deliver pre-specified assets (commodities, financials, etc.) at a certain date at a pre-agreed price
    • Underlying asset are well defined
    • Maturity is well known in advance
    • Futures price is set at the beginning
    • No cash exchange initially
      • Initial and maintenance margins are required
    • Profit and losses are settled daily
      • positions are “Marked to Market”
futures payoff
Futures Payoff
  • Imagine you manage an index fund and want to protect the value for the next year. You are long in the index, so wherever index goes, you go the same way:

Fund Payoff

Future Portfolio Value

Future Index Value

Current Value

futures payoff1
Futures Payoff
  • Now if you sell some futures contracts, let’s see what happens. When your portfolio value drops, the buyer needs to bring pre-agreed value, current value of the index. So you cover the difference!

Fund Payoff

Gains from

Futures

Position

Future Portfolio Value

Future Index Value

Losses

Future Payoff

Current Value

derivatives
Derivatives
  • Forward and futures are examples of derivatives; instruments that derive their value from some primitive like commodities, stocks, bonds, etc.
  • Major derivatives are:
    • Forward and Futures
    • Options
    • Swaps and Swaptions
    • Compound and Exotic Options
    • More advanced derivatives
options
Options
  • Bets on directional moves, up or down
    • Romans and Phoenicians traded options
    • Tulip mania in Holland was frothed with options, mostly “call” or right to buy
    • Early American options were called “privileges” and come under scrutiny after Great Crash of 1929
  • In 1973 two financial economists, Fischer Black and Myron Scholes devised a formula for pricing options. Shortly after CBOE was born.
    • Today CBOE and other regional option markets handle multi million dollar transaction of a variety of sorts.
option payoff
Option Payoff
  • Imagine again you manage an index fund and want to protect the value for the next year. You are long in the index, so wherever index goes, you go the same way:

Fund Payoff

Future Portfolio Value

Future Index Value

Current Value

option payoff1
Option Payoff
  • Now if you buy some put options, let’s see what happens. When your portfolio value drops, the put pays the strike price, say current value of the index. So you cover the difference again minus initial cost, of course!

Fund Payoff

Gains from

Option

Position

Future Portfolio Value

Future Index Value

Put Option Payoff

Losses

Current Value

hedging
Hedging
  • The process of eliminating or reducing the net impact of price fluctuation is called “hedging”.
    • Similar to “hedging” you bets so your losses are not devastatingly large!
  • A “perfect hedge” removes all volatilities!
    • Difficult and very expensive to implement
  • A practical hedge then can be an alternative. This is an attempt to reduce major swings while tolerating some fluctuation.
hedge hedge ratio
Hedge & Hedge Ratio
  • Steps toward a hedge:
    • Understanding distribution of value/cash flow
    • Defining tolerable level of short fall
    • Measure probability of short fall
    • Evaluating impact of derivatives
      • Evaluating what kind of contract is available
      • Measuring what kind of position needed
      • Determining how many contracts are needed
        • This is the Hedge Ratio, i.e., the number of contracts needed for every share (unit) of the underlying asset