The Candidate questions for the final exam.
1) • Please explain ‘short position’ when you construct your
portfolio. (page 171)
Let's imagine you have $1,000 to invest in two different things, Security A and
Security B. Normally, when you invest, you buy some of each (long positions). But,
here's the twist: you can also do something called "short selling." This means you
borrow some shares of one thing, sell them, and use that money to buy more of the
other thing.
For example, if you borrow $400 worth of shares of Security A and sell them, you get
$400. Now, you have your initial $1,000 plus the $400 from selling borrowed shares.
With this total, you buy more shares of Security B. So, you end up having more
invested in Security B than your original $1,000.
However, the tricky part is that you have to pay back the $400 you borrowed. So,
while you have more invested in Security B, you also owe $400. If everything stays
the same and you sell everything, you'd have $1,400 in total—$1,000 from your
initial investment and $400 from selling borrowed shares.
But, here's the catch: if the prices of Security A and Security B change while you're
doing all this, your total could be more or less than $1,000 when you sell everything.
So, it's a bit like a gamble, hoping the prices work in your favor!
2)• Please explain the figure 8.2. (p. 180)
Imagine you're building an investment portfolio with two assets, Security A and
Security B. Now, the concept of "locus" here represents different combinations of
how much you allocate to each of these assets.
We've drawn three loci, each representing a specific correlation between the returns
of Security A and Security B. Correlation is like a measure of how closely or loosely
these two assets move together.
Now, here's the fundamental idea: when you put all your money into just one of these
securities, the correlation between them doesn't matter. You get the return and risk of
that single asset. However, when you decide to diversify and spread your investment
between both A and B, the correlation becomes crucial.
If A and B tend to move independently or even in opposite directions, it's like having
a safety net. When one goes down, the other might go up, reducing the overall risk
(standard deviation) of your portfolio.
Now, let's talk about the curvature of these loci. The less curved the path, the less
risk you're taking on. It means that even with a fixed level of expected return, the
standard deviation (risk) of your portfolio decreases as the correlation between A
and B decreases.
Why does this happen? Well, when they're less correlated, one can potentially offset
the losses of the other. It's like having investments that act independently, offering a
form of risk reduction.
So, in a nutshell, these loci show you the trade-off between expected return and risk
in your portfolio, emphasizing how the correlation between your assets plays a
crucial role in shaping your overall risk exposure
3)• Please construct a riskless portfolio R using the following
information.
“Suppose that the rates of Securities U and V are perfectly
negatively (positively) correlated. Let Xu and Xv be the proportions
in which an investor allocates funds between these two securities
to construct Portfolio R. We shall now determine the values of Xu
and Xv that will make Portfolio R riskless.”
To construct a riskless portfolio, we take advantage of the perfect negative
correlation between Securities U and V. This means that when one goes up, the
other goes down, and vice versa.
Now, let's allocate funds between Securities U and V in proportions Xu and Xv to
create Portfolio R. To make this portfolio riskless, we want the movements of U and
V to cancel each other out.
In a perfectly negatively correlated scenario, the total risk of the portfolio is
minimized or even eliminated because the gains from one security offset the losses
from the other. Mathematically, we set up equations to ensure that the correlation
works in our favor:
This equation ensures that we invest all our funds in Securities U and V, covering the
entire portfolio.
Additionally, we consider the negative correlation by introducing the constraint:
Here, Puv represents the correlation coefficient between Securities U and V. In a
perfectly negative correlation, this term ensures that the risk from one security is
completely offset by the opposite movement of the other.
By solving these equations, we find the specific values for Xu and Xv that make
Portfolio R riskless, taking advantage of the unique characteristics of the negative
correlation between Securities U and V.
4)• Please explain arbitrage and equilibrium when two risky
securities have perfectly correlated rate of return. (p.197)
Imagine you have two types of investments, let's call them A and B. Now, in a
balanced situation (equilibrium), if investors think A and B are equally risky, they
should have similar expected returns. Why? Because if one is expected to give more
profit, everyone would rush to invest in that and the prices would change until the
expected returns are balanced.
Now, let's say you have two pairs of investments, U and V, and W and Z. In the first
pair, U and V move in opposite directions; if one goes up, the other goes down. In
the second pair, W and Z move in the same direction; if one goes up, the other goes
up too.
If there's a bank offering a return of 1%, and you can create a safe investment (like
Portfolio R or T) with a higher return using U, V, W, or Z, people will move their
money to these portfolios, affecting the prices of U, V, W, and Z.
For example, if you can create a portfolio that's more profitable than the bank with U
and V, people will buy U and V, making their prices go up and their expected returns
go down. If it's with W and Z, people will sell Z and buy W, making Z's price go down
and its expected return go up.
This process continues until the profits from these portfolios match the return from
the bank. It's like a balancing act where people adjust their investments until
everything evens out.
In a more advanced stage (chapter 14), they use this idea of perfect correlation to
figure out pricing for options, but that's a bit more complex.
5) Please explain how to derive Capital Market Line and interpret
the meaning of the Line.
In constructing the Capital Market Line (CML), the efficient frontier identifies
the optimal mix of risk and return for portfolios with only risky assets. The
market portfolio, found on the efficient frontier, represents this optimal mix.
Introducing a risk-free asset with a fixed return (Rf) allows us to draw a line
from Rf to the market portfolio, creating the starting point (tangency point M)
for the CML.
The CML encompasses all potential combinations of the risk-free asset and
the market portfolio. Investors can choose a point on the CML based on their
risk tolerance, with higher points indicating more risk and higher expected
returns.
The slope of the CML is crucial, signifying the additional return for increased
risk. A steeper slope implies more reward for the same rise in risk. The market
portfolio (point M) is optimal, as the line from Rf to M has a steeper slope
than any other line from Rf to alternative portfolios (e.g., Portfolio H on line K).
Portfolios on line K have counterparts on line M that offer either greater
return, lower risk, or both. Given typical investor preferences for more return
and less risk, selecting a portfolio on line K, like Portfolio H, would be
suboptimal compared to available alternatives on line M. The CML guides
investors in combining the risk-free asset with the market portfolio to achieve
their desired risk-return balance.
●
6)Please explain how to derive Security Market Line and interpret
the meaning of the Line.
In determining the conditions for an investor like Abigail to construct a portfolio
above the capital market line, we examine the allocation of funds between Security 1
and the market portfolio. Let X1 represent the proportion in Security 1, and 1X1 in the
market portfolio. The locus of risk-return combinations for portfolios containing
Security 1 and the market portfolio is concave, passing through points 1 and M.
The locus must be tangential to the capital market line at point M for equilibrium.
Lack of tangency allows opportunities for portfolios above the capital market line. If
the locus intersects the capital market line at point M from above, a point like S
contradicts market efficiency. Similarly, intersection at point M from below, as in
point T, is inconsistent with the capital market line.
Therefore, equilibrium requires tangency at point M. This ensures market efficiency
and leads to the equation of the security market line (SML). The SML acts as a
benchmark for evaluating securities, guiding investors in making informed decisions
based on the risk-return trade-off. Securities above the SML may be undervalued,
while those below may be overvalued. In essence, the SML aids in efficient resource
allocation in the market by considering the trade-off between risk and return.
7)•
(5) Explain what the characteristic lines are and how to
estimate beta.
8) •
(5) Explain a problem of agency by providing an example of
enforcing payouts of Free Cash Flows. (section 13.5)
The problem of agency, as described in the text, arises when managers have the
discretion to invest a firm's earnings in projects that may not necessarily maximize
shareholder wealth. In this context, free cash flow (FCF) represents the portion of net
earnings not paid in dividends and not invested in profitable projects.
Let's consider Firm K, which has an annual net earnings of $80,000. The firm invests
$50,000 in profitable projects and $20,000 in unprofitable projects. The remaining
$10,000 is paid out as dividends to shareholders. So, the annual FCF for Firm K is
$20,000 ($80,000 - $50,000 - $20,000).
Now, the shareholders want to ensure that the managers do not misuse the FCF by
investing in projects that do not cover their opportunity costs. One solution is to
introduce perpetual bonds into the capital structure. Suppose the firm sells bonds to
investors with an annual interest payment of $20,000, discounted at a rate of 0.12.
The aggregate price of the bonds would be $166,666.67.
By selling the bonds, the firm is constrained to use $20,000 of its net earnings to
make the annual interest payments. The shareholders receive a special, one-time
dividend of $166,666.67, which they can then invest themselves. Individual
shareholders may use their share of the special dividend to purchase some of these
bonds, obtaining a contractual right to their share of Firm K's annual FCF.
This strategy enforces payouts of FCF by restricting the managers' ability to retain
the entire FCF for potentially unprofitable projects. It aligns the interests of
shareholders and managers by channeling the FCF back to the shareholders, who
can make investment decisions based on their own opportunity costs. The
introduction of bonds creates a mechanism to discipline managers and ensure the
efficient use of the firm's earnings.
9)
Given the following information, please show the capital structure
of the two firms, and explain why the high debt equity ratio help the
firm to reallocating resources when consumers’ preferences change.
“Firm L has issued 500 bonds and 10,000 shares of (common) stock; Firm H has issued 800 bonds
and 10,000 shares of stock. The bonds issued by each firm have an annual coupon rate of .08 and a
face value of $1,000. Therefore, each firm is commit- ted to pay to the bondholders $80 per year on
each of its outstanding bonds. Since Firm L has issued 500 bonds, that firm must pay $40,000 per
year to its bondholders. Firm H, which has 800 bonds outstanding, must pay $64,000 per year to its
bondholders. Each firm generates net earnings of $100,000 per year. Firm L, which has only $40,000
of payments to make on its 500 bonds, has $60,000 for distribution to share- holders each year. By
comparison, Firm H has only $36,000 for distribution to share- holders each year; the remaining
$64,000 of its annual earnings is pledged to the investors who hold its 800 bonds. “
● Firm L:
● Bonds: 500
● Common Stock: 10,000 shares
● Firm H:
● Bonds: 800
● Common Stock: 10,000 shares
● Firm L Debt Equity Ratio: $40,000 (annual payment to bondholders) / $60,000
(available for shareholders) = 0.67 or 67%
● Firm H Debt Equity Ratio: $64,000 (annual payment to bondholders) / $36,000
(available for shareholders) = 1.78 or 178%
●
Firm L:
​VL = (500)($727.27)+(10,000)($42.86)
= $363,635+$428,600
= $792,235.00
.
●
Firm H:
very easy)
10)