12

The first metric to look at is house-price-to-rent ratios. Rental prices capture the value of the housing (and housing-linked) services provided by a property, including things like how safe a neighborhood is, how good the schools are, et cetera. In contrast, house prices are the capitalized value of the future stream of housing services PLUS the price of an ...


7

While it is possible to rigorously define a bubble in principle (see for example asset markets where prices violate transversality conditions), in practice it can be difficult or impossible to identify actual bubbles, even ex-post. For example, @dismalscience discusses looking at house-price-to-rent ratios. This sounds straightforward. If houses are ...


6

ICAPM Factors People have chosen different ways to pick factors. Chen, Roll and Ross are a classic example of attempts to find reasonable ICAPM factors. Fama-French factors are often explained as correlated with underlying ICAPM factors. Other researchers have chosen to look for factors without assuming outwardly observable exposures by analyzing returns ...


6

Using a simple textbook-approach, I will provide one possible answer here, showing that in this approach, the one thing that needs to be specified is "velocity of money" as regards sand dollars. I will use also the numerical values provided in the question, after cutting out six zeros. I assume that the Law of One Price holds, so $$P_s\cdot S_{USD/s} = P_{...


5

All you need for this particular question is the following. Let $\mathbf{X}$ be a $T \times K$ matrix, $\mathbf{w}$ a K-dimensional vector and $\mathbf{y}$ a T-dimensional vector, then $$ \begin{eqnarray*} \frac{\partial \mathbf{w}^{\prime}\mathbf{X}^{\prime}\mathbf{y}}{\partial \mathbf{w}}&=& \mathbf{X}^{\prime}\mathbf{y}\\ \frac{\partial \mathbf{w}...


5

Let's ignore for the moment the existence of the expected value. If this was a deterministic set-up, linearization through taking logs would be straightforward, and without the tricks of the links the OP provided. Taking natural logs on both sides of the first equation we obtain: $$0 = \theta \ln \delta-\frac {\theta}{\psi}\ln \left (\frac{C_{t+1}}{C_t} \...


5

With apologies for the somewhat journalistic answer (as others have noted, even defining a bubble in a rigorous fashion is difficult). Information on housing supply may be of some use. Demand for housing is quite inelastic (everyone needs somewhere to live) so shifts in supply should show up mostly in prices and less in market quantities. As an example, ...


5

What are volatility swaps? Before the introduction of what is now volatility swaps, investors gained exposure to the market's volatility (yes, they already wanted to) through call and put options, products that depend on volatility, but also heavily on the price level of the underlying asset. A volatility swap is a forward contract on future realized price ...


5

The recommended books are decent. From these two I'd go with Bailey first and if you're comfortable with that, then LeRoy & Werner. The latter requires some background in linear algebra and optimization theory. If you want to study some econometric applications for financial economics, you might try: Cuthbertson & Nitzsche: Quantitative Financial ...


5

Examples where this happens are always extreme and contrived. I can think of two kinds of examples. The first is where you have an asset that for some reason has a price of zero or negative but a positive payoff in some states (perhaps no other asset pays off in that state). The second is where you have two assets with positive prices that have negative ...


5

Net Present Value (NPV) as a soft concept existed probably even in antiquity but it was formalized and made popular by Irving Fisher in his book the Rate of Interest. Internal rate of return is basically a special application of NPV. It was also first formally introduced in Fisher's book although he called it 'rate of return over costs'. Duration of bonds ...


5

...no-arbitrage models (such as Black-Scholes and HJM) are equivalent to equilibrium models (such as CAPM or C-CAPM). Short Answer Yes, for models where asset prices are assumed to be Ito semimartingales (where the martingale part is a Brownian integral), although a more general argument is needed than that suggested by the special cases typically ...


4

It's actually quite easy. The key things to know are 1) that the majority of house purchases are made via mortgage lending, and that 2) an excess of bank lending over bank loan repayment causes money creation. So first determine if there is an abnormally high increase in the supply of money occurring - if yes, then there is a bubble, and if not, then the ...


4

How about a hint rather than an exact answer? Put Call Parity concerns the relationship between the prices of European put and call options (with matched strike and expiration dates): $$ C - P = D(F-K) $$ where C and P are the current prices of calls and puts respectively, D is the discount factor, F is the forward price of the asset, and K is the strike ...


4

The way I would think of this is as follows. Let us write the value of the first company as $V_{A}$and the second as $V_{B}.$ Given your definition, let me know if you agree with the following argument: $$ V_{A}=s_{AA}\sum_{t=0}^{\infty}\pi_{tA}+s_{AB}\sum_{t=0}^{\infty}\pi_{tB} $$ Where $s_{AA}$ denotes the time invariant share of company A that comapny A ...


4

$\newcommand{\dd}{\, \mathrm{d}}$ If we apply Ito's lemma, then \begin{align*} \dd \xi_t &= -\xi_t \dd X_t + \frac 12 \xi_t (\dd X_t)^2\\ &= -\xi_t \left(\frac 12 \lambda_t^2 \dd t + \lambda_t \dd z_t\right) + \frac 12 \xi_t \lambda_t^2 \dd t \\ &= -\xi_t \lambda \dd z_t. \end{align*}


4

As regards the first question, the "$p_t=...$" expression is conceptually and qualitatively useful because, at the optimum, it relates price with consumption and expectations. Mathematically it is an implicit function of course, so it is not a "closed-form solution" to "tell us how to find $p_t$". Cochrane acknowledges this as he writes in p. 6 "We have ...


4

Imagine: I borrow 1 bitcoin from you and agree to pay you back $(1+r)$ bitcoin in a month. I immediately sell the bitcoin you lent me. One month from now, I buy $(1+r)$ bitcoin and pay you back. If I can conduct those transactions, I can short sell bitcoin.


4

It seems to me that we might as well say that markets are complete. It seems to me to be somewhat inconsequential since this is a representative agent model and that market clearing requires that the only assets that the agent may hold in positive net supply are the $n$ trees. The prices of all Arrow-Debreu securities may be inferred from shadow prices. ...


3

The value of a tradeable good is equal to what the marginal buyer will pay for it. I will explain further, but first let me correct one misconception in your question. You state: Now, once you buy a car, the value of the car depreciates once you drove it outside of the factory. For example, price of a new 6000 dollars car, will be 5800 dollars. Although, ...


3

In Keynes's Treatise on Money he argued that the phenomenon you describe, known as "normal backwardation", is due to the fact that certain commodities producers hedge their price risk (importantly, they hedge their risk much more than consumers) by selling futures. The intuition for why the producer does this is that it allows the producer to lock in the ...


3

The investor has erroneously overvalued the value of the stock/commodity. Here is a prominent paper that models irrational bubbles: This paper attempts to formalise herd behaviour or mutual mimetic contagion in speculative markets. The emergence of bubbles is explained as a self-organising process of infection among traders leading to equilibrium ...


3

I'll direct you to wikipedia which has some pretty good information about it. One of the important things about speculative bubbles is that they are very difficult to identify before they burst. It is very difficult to say the market is overvaluing an asset or a change in economic conditions have raised the true value. That said, there are some signs that a ...


3

Generally: $P(f\in[10,20]) = P(120 \leq S_t \leq 130) = P(S_t \leq 130) - P(S_t \leq 120)$ That is, the probability that the option is between 10 and twenty is the same that the stock is between 120 and 130. The probability that the stock is between 120 and 130 is the probability the stock is less than 130 minus the probability that it is less than 120. If ...


3

First, you are in fact given $p$. You can think of return as a security that costs 1 in current period and pays off $R$ in the next period. The price vector and the payoff matrix are thus $$ p = \begin{bmatrix} 1 \\ 1 \end{bmatrix}, \ X = \begin{bmatrix} 1.1 & 1.0 & 0.9 \\ 1.0 & 1.0 & 1.0 \end{bmatrix} $$ and we need to find positive vector ...


3

If you want to describe excess returns in terms of exposure to common risk factors, you want the risk factors to be orthogonal. However, if you have $k$ factors with no perfect collinearity, you can always orthogonalize them and use those. You then call the orthogonalized factors the risk factors.


3

Say you have a portfolio with returns described by a random variable X. Call the lowest possible realization of X: xmin. If you take a levered position in that portfolio with leverage A and financing cost r your returns are r(A-1)+AX. There will exist a value of A no larger than 1/xmin where when you get the worst return of X and the levered portfolio ...


3

Your problem seems like asset-pricing equation with recursive (Epstein-Zin) preferences. When interested in asset prices, one has to be careful with the usual "macroeconomic" linearization. Such an approximation is certainty-equivalent, meaning that coefficients of linearized solution do not depend on size of shocks. Moreover, all variables in linearized ...


3

The correct approximation is $f(x) \approx E[f(x)] + E[f'(x)] (x - E[x])$. This is unbiased, whereas $f(x) \approx E[f(x)] + f'(E[x]) (x - E[x])$ is not. To see this, project $f(x) - \overline{f(x)}$ on $x - \bar x$, where the "bar" represents the expectation operator. Then, approximate $$ \frac{\text{Cov}(f(x), x)}{\text{Var(x)}} \approx E[f'(x)]. $$ This ...


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