Portfolio Theory and Financial Markets
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Questions and Answers

What is the significance of the left boundary of the feasible set in portfolio theory?

  • It represents the least risk investment option.
  • It is where the risk-seeking portfolios lie.
  • It is known as the minimum variance set. (correct)
  • It indicates the maximum return achievable.

    • Which type of investor is primarily interested in minimizing variance while maximizing return?

  • A risk-averse investor. (correct)
  • A risk-seeking investor.
  • An indifferent investor.
  • A speculating investor.

    • What characterizes portfolios that lie on the efficient frontier?

  • They have the potential for unlimited risk.
  • They offer the highest return for a given level of risk. (correct)
  • They are guaranteed to yield positive returns.
  • They only include low-risk investments.

    • In the context of portfolio optimization, what does the symbol $r̄$ signify?

    <p>The mean return of the portfolio.</p> Signup and view all the answers

    What assumption is made regarding weights in the portfolio when allowing short selling?

    <p>Weights can assume both positive and negative values.</p> Signup and view all the answers

    Which of the following statements is true about the relationship between risk-averse investors and the minimum variance point?

    <p>They tend to choose the minimum variance point as their investment strategy.</p> Signup and view all the answers

    What does the term 'join' refer to when discussing arbitrary pairs of points in portfolio theory?

    <p>The line connecting two asset combinations.</p> Signup and view all the answers

    What effect does fixing the standard deviation of the portfolio return have on investors' preferences?

    <p>They will focus on achieving the highest return possible.</p> Signup and view all the answers

    What is the main advantage of inflation products in relation to interest rates?

    <p>They are linked to real rates of interest, compensating for inflation.</p> Signup and view all the answers

    Which index is primarily used in the Euro zone for inflation measurement?

    <p>Harmonised Index of Consumer Prices (HICPxT)</p> Signup and view all the answers

    What characterizes a perpetual annuity?

    <p>It pays a fixed amount each year forever.</p> Signup and view all the answers

    How is the present value of a perpetual annuity calculated with a per-period interest rate?

    <p>It uses the formula $P = \frac{A}{r}$.</p> Signup and view all the answers

    What happens when interest rates are continuously compounded in calculating the price of a perpetual annuity?

    <p>The same formula applies yielding same results.</p> Signup and view all the answers

    What is an example of a perpetual annuity that was commonly found in the UK?

    <p>Consolidated Annuities (consoles)</p> Signup and view all the answers

    Which statement concerning fixed-income instruments is correct?

    <p>They typically pay a stream of equal periodic cash flows.</p> Signup and view all the answers

    What is the significance of the cash flow being linked to an inflation index such as the CPI?

    <p>It ties the payments directly to real purchasing power.</p> Signup and view all the answers

    What does the yield to maturity represent for a bond?

    <p>The internal rate of return based on current price.</p> Signup and view all the answers

    How is the price of a bond (P) calculated according to the formula provided?

    <p>P = F / (1 + R)^n + c * (1 - (1 + R/m)^-n)</p> Signup and view all the answers

    What effect does maturity (T) have on the bond price's sensitivity to interest rate changes?

    <p>Sensitivity increases linearly with maturity.</p> Signup and view all the answers

    What is the formula for calculating the future value of a cash flow stream in an ideal bank?

    <p>F V = x0(1 + r)n + x1(1 + r)n−1 + ... + xn</p> Signup and view all the answers

    What is the definition of duration in the context of fixed-income instruments?

    <p>The weighted average time of cash flows.</p> Signup and view all the answers

    How is the present value of a cash flow stream calculated?

    <p>P V = x0 + x1/(1 + r) + x2/(1 + r)2 + ... + xn/(1 + r)n</p> Signup and view all the answers

    What does the internal rate of return (IRR) represent in relation to a cash flow stream?

    <p>The rate that makes the present value of the cash flows equal to zero.</p> Signup and view all the answers

    In the absence of coupon payments, what is the price of a bond with a continuously compounding rate?

    <p>P = e^(-rT)</p> Signup and view all the answers

    Which statement about ideal banks is correct?

    <p>Ideal banks offer identical interest rates for both deposits and loans.</p> Signup and view all the answers

    What happens to the price of long-dated bonds when interest rates change?

    <p>They are more sensitive to interest rate changes.</p> Signup and view all the answers

    What determines the weighting coefficients in the duration calculation?

    <p>The present values of individual cash flows.</p> Signup and view all the answers

    What is the role of the variable r in financial calculations described?

    <p>It denotes the interest rate for the compounding period.</p> Signup and view all the answers

    When determining the internal rate of return, what equation must be satisfied?

    <p>0 = x0 + x1/(1 + r̄) + x2/(1 + r̄)2 + ... + xn/(1 + r̄)n</p> Signup and view all the answers

    If a bond pays $c$ in coupon payments and has a yield $R$, how is this reflected in the bond pricing formula?

    <p>It increases the present value of the bond.</p> Signup and view all the answers

    What complicates the analysis of real banks compared to ideal banks?

    <p>Real banks have fluctuating interest rates for deposits and loans.</p> Signup and view all the answers

    Why is the internal rate of return not defined based on the prevailing interest rate?

    <p>It solely depends on the cash flow characteristics of the investment.</p> Signup and view all the answers

    Why should the price of a perpetual annuity decrease as the interest rate increases?

    <p>Increasing rates reduce the present value of future cash flows.</p> Signup and view all the answers

    What is the expression for the present value of a finite payment stream given a fixed interest rate r?

    <p>$P(n) = A \frac{(1 - (1+r)^{-n})}{r}$</p> Signup and view all the answers

    What happens to the present value of an annuity when the interest rate is allowed to vary over time?

    <p>The present value fluctuates based on the interest rate dynamics.</p> Signup and view all the answers

    In the case of a constant interest rate, which expression is equivalent to the present value of an annuity?

    <p>$P(T) = A \frac{1 - e^{-rT}}{r}$</p> Signup and view all the answers

    What is the integral form used to calculate the present value of an annuity with interest rate r varying over time?

    <p>$P(T) = A e^{-\int_0^T r(s) ds}$</p> Signup and view all the answers

    How does a higher interest rate impact the future value of annuity payments?

    <p>It reduces the future value of those payments.</p> Signup and view all the answers

    What implications do interest rate dynamics have on the pricing of annuities?

    <p>They make annuities far less predictable in value.</p> Signup and view all the answers

    Study Notes

    Portfolio Theory

    • The join of two points in a feasible set never crosses the left boundary.
    • The left boundary of a feasible set is called the minimum variance set.
    • Minimum variance portfolios minimize risk.
    • Investors are risk-averse when they prefer portfolios that minimize variance.
    • Risk-seeking investors accept higher potential variance for higher returns.
    • The efficient frontier is the upper-left portion of the feasible set.
    • The Markowitz model finds minimum-variance portfolios.
    • The model assumes short-selling is possible.
    • The mean portfolio return is fixed and then variance is minimized.

    Financial Markets and Derivative Pricing

    • Ideal banks have equal deposit and loan rates and no transaction fees.
    • Future value of cash flow is calculated by compounding each cash flow forward.
    • Present value of cash flow is calculated by discounting each cash flow back.
    • The internal rate of return (IRR) is the rate that makes the present value of a cash flow equal to zero.
    • Pension benefits often come in the form of annuities.
    • Inflation-linked products use inflation indices like the consumer price index (CPI) to adjust payments.
    • Perpetual annuities are a series of fixed payments that continue indefinitely.
    • Consoles are UK government bonds that pay a fixed amount forever.
    • The price of a perpetual annuity is the fixed payment divided by the interest rate.
    • The price of an annuity with a finite lifetime decreases as the interest rate increases.
    • The price of an annuity with a varying interest rate is calculated by integrating the present value of each cash flow.
    • Yield to maturity is the internal rate of return of a bond at the current price.
    • The price of a bond is determined by the face value, coupon payments, yield to maturity, and time to maturity.
    • Long-dated bonds are more sensitive to interest rate changes than short-dated bonds.
    • The duration of a fixed-income instrument is the weighted average of the times that cash flows are made, with weights based on the present values of each cash flow.

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    Description

    This quiz covers essential concepts in portfolio theory, focusing on risk minimization and the efficient frontier. It also delves into financial markets, including the valuation of cash flows and the internal rate of return. Test your understanding of these fundamental financial principles.

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