2017 A №1
a) What are the operational and systemic risks? How can we manage these risks? p82
Operational risk: the risk of fraud or failures in operations due to systems breaking down or human errors
being made / associated with internal operational processes.
Operational risks are managed by putting in place safeguards within the firm or purchasing insurance
products that can limit losses.
Systemic risk: the risk of meltdown in the financial system, for instance caused by a chain reaction of events
causing liquidity crises or defaults / associated with external systemic factors that threaten the financial system
on which the corporation depends
Systemic risks are managed usually by a regulator that seeks to strengthen key institutions that are important
for maintaining the financial system as well as identifying and taking actions that threaten the financial system
but which do not arise from any single firm’s actions.
b) Consider a stock with expected return 11.4%. The beta of this stock is 1.2, its Jensen’s alpha is 0, and
the risk free rate is 3%. The variance of the market portfolio is 0.09, and the variance of the stock is
0.2. What are the systematic and the unsystematic variances of the stock?
total return = risk-free return + a risky return that depends on the market risk + a risky return that is
independent of the market risk:
r=r
f+β rM+ε
Var (r )=0+β2 var(rM)+var (ε)
0.2=1.22∗0.09+var (ε)
systematic risk β2 var(rM)=1.22∗0.09=0.1296
unsystematic risk var (ε)=0.2-0.1296=0.0704
c) Suppose there are 20 stocks in total with the same beta, alpha and variance as the stock in (b), and
assume the idiosyncratic risk terms are uncorrelated across the stocks. What are the systematic variance
and the unsystematic variance of an equally weighted portfolio of the 20 stocks?
20 stocks
r
i=rf+βi rM+εi
βi=β p
r
p=rf+βp rM+εp
Var(rp)=0+β2p var (rM)+var (ε p)
systematic risk β2p var (rM)=0.1296
Var(εp)=Var(20 1 ε1)+…+Var(20 1 ε20)=Var(20 1 ∑20 1 εi)=20Var(20 1 εi)=20(20 1 )2Var (εi)=20(20 1 )20.0704=0.00352
unsystematic risk var(εp)=0.00352
2017 A №2
a) What are an upward-sloping and an inverted term structures of interest rates? Discuss the expectation
hypothesis and the liquidity preference theory of the term structure of interest rates. p70
The collection of spot rates of various maturities are called the term structure of interest rates.
Upward-sloping shape, positive, or rising, in which short rates are very low, with long rates substantially
higher.
Inverted shape, downward-sloping or negative, in which short rates are high with long-term rates are
significantly lower.
There are several hypotheses put forward to explain the shape of the term structure.
Expectations hypothesis states that the slope in term structure reflects the market’s expectations about future
interest rates. This means that the forward rates we observe today are where we expect the future spot rates
will be.
Liquidity preference theory states that the longer yields reflect higher risk, and must therefore offer higher
returns to the investors.