Skip to main content
6 votes

Is forward price trendless under the real-world measure?

Definitions For fixed $T$ and moving $t \leq T$ then by definition $\color{blue}{(*)}$, forward prices $F(t,T)$ and future prices $\text{Fut}(t,T)$ are both conditional expectations. However, these ...
Quantuple's user avatar
  • 14.7k
6 votes
Accepted

The positivity of the market price of risk

No, it can be negative. The price of risk is what you agree to receive on average in exchange for positive returns when the risk measure is high, and determined by the covariance of the risk measure ...
Igor Pozdeev's user avatar
5 votes
Accepted

Why exposure to the profitability factor increases investment premium?

As @skoestlmeier and @noob2 commented there's much research going on about the profitability anomaly. Firstly, there are different ways of measuring profitability. Novy-Marx (2013, JFE) uses gross ...
Kevin's user avatar
  • 16k
5 votes
Accepted

What is time-varying risk premium? Forecasting stock returns

Another way of staying "time-varying risk-premium", is saying that the risk-premium is predictable. However, that the fact that the risk-premium is predictable does not means that you can make money ...
phdstudent's user avatar
  • 8,381
4 votes
Accepted

Definition of factor premium: against cap weighted index or against treasury bills?

All factor returns (including "passive" factors like equity premium, credit premium etc) should be assessed using the fairest possible basis for comparison - self-financing portfolios. For a passive ...
Chris Taylor's user avatar
  • 5,931
4 votes

Intuitively, why does liquidity premium contribute to bond yield?

For clarity, I'll use two expressions, "liquidity premium" and "illiquidity premium": "Liquidity premium" arises when investors value the liquidity profile of an instrument so much that they are ...
Helin's user avatar
  • 11.7k
4 votes
Accepted

Behavioral SDF: modelling sentiment risk premium

Maybe it is not exactly what you are looking for, but you can take a look at this paper by Kozak, Nagel and Santosh. Roughly speaking, we know that the first order conditions of arbitrageurs must be ...
fni's user avatar
  • 1,896
4 votes

How to determine the risk premium from the Vasicek one factor model?

I recommend two papers that should help you with this exercise. The first is "Kalman Filtering of Generalized Vasicek Term Structure Models." This paper provides a general framework for ...
Helin's user avatar
  • 11.7k
3 votes

If equity returns are normally distributed, why are average equity returns not zero

Well there are two misconceptions in your assessment of how returns behave. 1) Returns can be normally distributed or not; 2) Even if they are normally distributed it does not mean that returns ...
phdstudent's user avatar
  • 8,381
3 votes
Accepted

Low volatility in factor regression

The CAPM claims that only systematic risk matters (i.e. covariation with the market) to determine an asset's expected return. So the fact that low volatility stocks have returns that are not ...
Kevin's user avatar
  • 16k
3 votes
Accepted

What should happen to the equity risk premium as rates change?

There does not seem to be a clear relationship between interest rates and equity risk premiums. Damodaran (2019) has a great paper that goes into details of equity risk premiums. In this work, he ...
AK88's user avatar
  • 1,840
3 votes

If equity returns are normally distributed, why are average equity returns not zero

It's news to me that in today's world anybody really believes that equity returns are normally distributed. For instance in US Senate testimony by a Goldman Sachs CFO, under assumptions of Gaussian ...
DJohnson's user avatar
  • 169
3 votes

What is time-varying risk premium? Forecasting stock returns

Up until the work of Robert Shiller in about 1980, it was thought that the expected excess return on the market $(R_M−R_f)$ is constant and is an equilibrium risk premium. Shiller showed that this is ...
Alex C's user avatar
  • 9,382
3 votes

Debunking risk premium via "hedging" argument? (or why even in the real world $\mu$ should equal $r$)

The most rigorous approach I have seen so far eliminating the risk premium is this one: Emanuel Derman: The Perception of Time, Risk and Return During Periods of Speculation (2002) Equation 2.23 on ...
vonjd's user avatar
  • 27.5k
3 votes
Accepted

Market price of risk of different maturities

What @noob2 said: Actually there is empirical evidence of the opposite, i.e. the existence of a Term Premium. But this is not evidence of arbitrage, just that a more complicated risk model than ...
demully's user avatar
  • 5,071
2 votes

How to calculate unsystematic risk?

Unsystematic risk of a single stock can be calculated as follows: $$\sigma_\lambda-\rho_{\lambda,m}\sigma_\lambda=\sigma_\lambda(1-\rho_{\lambda,m})$$ where $\sigma_\lambda$ is the volatility of ...
vonjd's user avatar
  • 27.5k
2 votes

How to calculate unsystematic risk?

I have studied unsystematic risk [USR] for more than two decades. In fact, I wrote a book (which is here) whose central focus is how to deal with USR in the valuation of non-public companies. It is a ...
Warren Miller's user avatar
2 votes

Why should there be an equity risk premium?

This one is far from straight-forward, although bear with me. It is possible to infer from first principles an ERP reasonably close to normative consensus expectations. The attached from Howard ...
demully's user avatar
  • 5,071
2 votes
Accepted

Is it possible to approach finding the risk premium of this derivative using Ito's Lemma?

Assume that under the real world measure $$ dS_t/S_t = (\alpha-\delta) dt + \sigma dZ_t^\Bbb{P} \tag{1} $$ Under the EMM $\Bbb{Q}$ one then needs to have (fundamental theorem of asset pricing: in the ...
Quantuple's user avatar
  • 14.7k
2 votes
Accepted

Short-rate models: Risk-premium of $T$-bonds

Imagine you hold a zero coupon bond with a certain maturity $T$ and the short rate follows a process like you specified. You might know deterministically what the cash bond pays this period, but you ...
spaceisdarkgreen's user avatar
2 votes

If equity returns are normally distributed, why are average equity returns not zero

Normality does not mean that mean return has be zero. The assumption you are talking about is of standard normal distribution which has mean and SD (0,1) respectively. As your question indicates ...
Ashutosh's user avatar
2 votes

If equity returns are normally distributed, why are average equity returns not zero

A distribution may be normal and have a mean different from zero. For example, IQs, weights, heights and so forth. All normal distributions assume a mean and a standard deviation. These two parameters ...
rmacey's user avatar
  • 196
2 votes

Why exposure to the profitability factor increases investment premium?

In addition to @KeSchn excellent answer i will provide the original intent by Fama/French as they proposed the "Profitability" factor in their 2015 paper "A five-factor asset pricing ...
skoestlmeier's user avatar
  • 2,916
2 votes

How to determine the risk premium from the Vasicek one factor model?

With only a short rate $r_t$ (not a tradable asset) given, we have a context where there is no risky asset, but there is at least one Brownian motion driver (incomplete market model). The only traded ...
ir7's user avatar
  • 5,043
1 vote

How is the risk premium of the index estimated?

Estimating ex-post risk premium is easy. Estimating ex-ante risk premium, on the other hand, is the holy grail of investing and is incredibly difficult. As @noob2 has mentioned, if you assume that ...
Helin's user avatar
  • 11.7k
1 vote
Accepted

What is risk premium of a portfolio?

This intuition is correct. Formally, we consider that people are risk averse which is just another way of saying that they prefer more stable to less stable cash flows. Another equivalent way of ...
Stéphane's user avatar
  • 2,476
1 vote
Accepted

Value premium analysis - Equal or Value-weighted Portfolios?

In principal, nothing stops you from doing both, constructing equally weighted and value weighted portfolios and see how the results differ :) In principal, I'd advice to use value weighted ...
Kevin's user avatar
  • 16k
1 vote
Accepted

Is there a robust way to calculate stock beta or factor exposure that's specific to crashes?

Within the framework you are proposing, it would make no sense. It would be failing to distinguish noise from signal. Extreme events are rarely triggered by measures of central tendency. It is like ...
Dave Harris's user avatar
  • 4,299
1 vote
Accepted

Estimation of market price of risk of short interest rate under the Hull-White model

There's a large literature dedicated to this topic. The following two methods are my preferred (they also happen to be the most popular): Kim and Orphanides's Term Structure Estimation with Survey ...
Helin's user avatar
  • 11.7k
1 vote

Intuitively, why does liquidity premium contribute to bond yield?

I do not find convincing the argument that the yield curve is upward sloping due to the lack of a secondary market for longer dated securities. In fact, there is a highly liquid market for 2yr, 5yr, ...
dm63's user avatar
  • 17.2k

Only top scored, non community-wiki answers of a minimum length are eligible