Download Risk Management - Spears School of Business

Measuring Risk
Risk Management
Prof. Ali Nejadmalayeri,
a.k.a. “Dr N”
Risk & Return of Securities
• Assuming that current price is P0 and the security
can be sold for P1, then:
P1
r  1
P0
• If this return is random, then over time, we can see
what is its distribution. The central tendency of
the distribution is mean. If this distribution is true
and stable, then this mean is our measure of
expected value, E[r]. One measure of variation of
our random return is variance, E[r – E[r]]2.
• Another measure of volatility is standard
deviation which squared root of the variance.
Probability & Distribution
• Given that we know the distribution of returns,
then we can compute cumulative probabilities of
returns being below certain thresholds!
Excel & CDFs
• Imagine, IBM has an average return of 10%
and standard deviation of 30%. What is
probability of a loss?
– Use NORMDIST function in Excel
• Enter
CDF vs. PDF
• Cumulative Distribution Functions represent
probability of up to an outcome whereas
Probability Density Functions represent
probability of one outcome!
Portfolio Return
• Imagine N assets with returns, ri, are combined
such that wi fraction of total funds is invested in
each of the assets, then the portfolio’s return is:
N
rp   wi ri
i 1
• Then for expected return of the portfolio, we have:
N
E[rp ]   wi E[ri ]
i 1
Portfolio Variance
• Imagine that each pair of assets in a portfolio with
N assets with returns, ri, and asset weight, wi, has
a correlation of ρij, then the variance of the
portfolio is:
N
Var[rp ]   w Var[ri ]
i 1
N

i 1
2
i
N
w
j 1
i
w j Var [ri ] Var [rj ]  ij
0.5
0.5
Diversification
• Unlike return, variance of a portfolio is also
related to correlations. So if these
correlations different from ONE, then there
can be some risk saving!
Efficient Frontier
• When assets are combined, the possible return-risk
outcomes form an efficient frontier on which best
return for any level risk or vice versa lowest risk
for any level return is obtained!
Risk & Asset Pricing
• If idiosyncratic risk can be removed by creating
well-diversified portfolios, then only correlations
with market risk should matter for determining
return!
M
 M
Var[rm ]  Cov[rm , rm ]  Cov wi ri , rm    wi Cov[ri , rm ]
 i 1
 i 1
• Then return on each asset is given by:

E ri   rf   i E rm   rf
Cov[ri , rm ]
i 
Var[rm ]

Valuation & CAPM
• Assume a firm generates E[C] of cash
flows. If the firm is all equity financed, then
value of the firm is defined by:
E C 
E C 
V

E ri  1  rf  i E rm   rf


Risk Management & Value
• If risk management reduces risk, then value
can increase; lower discount rate!
– By prudent diversification schemes,
idiosyncratic risk can be eliminated
• In perfect markets, both investors and firms can do
this, so the shouldn’t be reward associated with risk
management in perfect markets
– By taking short or offsetting positions,
systematic risk can be eliminated
• In perfect markets, both investors and firms can do
this, so the shouldn’t be reward associated with risk
management in perfect markets
Why Manage Risk?
• Hedging Irrelevance Proposition:
– When the cost of bearing risk is same for firms
and individuals, hedging cannot add value!
• Risk management is only beneficial only if
firms can perform hedging at lower cost
than their shareholders.
A Helicopter View
• Uncertainty is a fact of life, so there is no crystal
ball! But risk can be managed!
Indentify Risk Exposures
Measure and Estimate
Risk Exposures
Asset Effects of Exposures
Find Instruments & Facilities
to Shift or Trade Risk
Assess Costs & Benefits of
Instruments
From a Risk Mitigation Strategy:
Avoid, Transfer, Mitigate, Keep
Evaluate Performance
Topology of Risk
Market Risk
Credit Risk
Liquidity Risk
Risks
Operational Risk
Legal &
Regulatory Risk
Business Risk
Strategic Risk
Reputation Risk
Financial Risks
Equity Price Risk
Market
Risk
Trading Risk
Interest Rate Risk
Currency Risk
Commodity Risk
Financial
Risks
Credit
Risk
Transaction Risk
Portfolio
Concentration
Gap Risk
General
Market
Risk
Specific
Risk