A reader recently asked an important question, one which often puzzles those new to quantitative finance (especially those coming from technical analysis, which relies upon price pattern analysis):

Why use the logarithm of returns, rather than price or raw returns?

The answer is several fold, each of whose individual importance varies by problem domain.

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Source: 中金网产业数据库 http://ceidata.cei.gov.cn/aspx/Default.aspx

Balance Sheet of Other Depository Corporations (People’s Bank of China, 2011)



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  1. Slowing emerging market growth → commodity prices (particularly metals) → impacts on trade balances and challenges from a more balanced and sustainable growth path in China for metal and energy exporters.
  2. U.S. energy boom.

Recent Developments and Impact of Emerging Market Slowdown

1)      Metals: steep fall in metals prices ←continuing rise in metals mine supply + slowing real estate sector in China.

2)      Oil: price remained $105 a barrel (coal and natural gas ↓).

Elevated crude oil prices have played a role in keeping food prices relatively high because energy is an important cost component (China reliant on world markets for oilseeds).

  •  [Chart] First-round trade balance impact from changes in commodity prices (30% metals price drop & 10% energy price drop)

3)      Impacts of growth path in China on commodity demand: in the short run, as demand shifts away from materials-intensive growth some commodity exporters could be vulnerable. There is particular concern about the spillover effect of demand rebalancing in China.

  •  [Chart] Impact of Chinese demand slowdown on commodity exporters


Price Outlook and Risks

  • IMF’s outlook:
  • Petroleum: $104.5 (2013) → $101.4 (2014)
  • Food: also increase slightly in 2013 but decline by 6% in 2014
  • Metals: decrease by 4% in 2013 and 5% in 2014
  • Concerns over spikes of oil prices

Economic Impacts of the U.S. Energy Boom

  • The U.S. is experiencing a boom in energy production. Natural gas output increased 25%, crude oil and other liquids increased 30% during the past 5 years, reducing net oil imports by nearly 40%.
  • Assume there is an increase in energy production over the next 12 years, U.S. real GDP will increase by 1.2%, employment increases by 0.5%.
  • Most impact on GDP and small impact on current account is that the share of energy in the economy remains quite small.

Link: http://www.imf.org/external/np/res/commod/pdf/cmr/cmr1013.pdf



This paper examines the correlation between stock and bond returns. It first documents that the major trends in stock-bond correlation for G7 countries follow a similar reverting pattern in the past forty years. Next, an asset pricing model is employed to show that the correlation of stock and bond returns can be explained by their common exposure to macroeconomic factors. The link between the stock-bond correlation and macroeconomic factors is examined using three successively more realistic formulations of asset return dynamics. Empirical results indi- cate that the major trends in stock-bond correlation are determined primarily by uncertainty about expected inflation. Unexpected inflation and the real interest rate are significant to a lesser degree. Forecasting this stock-bond correlation using macroeconomic factors also helps improve investors’ asset allocation decisions. One implication of this link between trends in stock-bond correlation and inflation risk is the Murphy’s Law of Diversification: diversification opportunities are least available when they are most needed.

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=363641

This paper focuses on the dynamics of cross-correlations and conditional risk premia.

Return correlations between assets with different amounts of cash-flow risk exhibit substantial variation over time. This paper argues that this variation in correlations is likely to manifest in the assets’ risk premia, however, the sources of risk premia and time-variation in correlations in financial markets are not yet well understood. This paper attempts to discover the economic mechanisms that drive risk premia on different asset classes.

The author specify two technologies with different amounts of capital risk and adjustment costs to investment. The two technologies can be considered as low-risk companies and hi-risk companies.

When one technology has a good shock, investors want to rebalance towards the other technology. However, they face adjustment costs, which drives up the price of the technology with no shock. This mechanism is called rebalancing, which produces a positive correlation between returns on the two technologies, even when they have different cash flows (similar to Cochrane et al 2008’s “two trees”).

The model also features another mechanism: flight-to-safety effect as a result of the time-varying risk-aversion that investors move from the riskier to the less risky technology, which produces a negative correlation between returns on the two technologies.

The authors argues that when risk aversion is high, the flight-to-safety mechanism dominates, driving the correlation between bond and stock returns and real bond risk premium negative; when risk aversion is low, the rebalancing mechanism dominants and results in a positive correlation  between bond and stock return and a positive term premium. 

Rebalancing relies on slow physical capital reallocation and thus drives low frequency dynamics. Flight-to-safety operates at higher frequencies and drives most of the variation in financial variables in the model.

Therefore rebalancing and flight-to-safety result in time-varying correlation between returns on assets with different amounts of cash-flow risk, that potentially changes sign, even when their cash flows are independent.

This paper also shows empirical and model-implied proxies for risk aversion, which is measured through credit spreads, VIX, investors fear index by Bollerslev and Todorow (2011).

Model: General Equilibrium Model

Data: 1980-2012

Abstract: I use a general equilibrium model to jointly explain the time-variation in real bond and stock risk premia along with time-variation in the comovement of realized returns. The model features multiple investment technologies and produces stock and real bond return correlation which changes both in magnitude and sign. The model also delivers a time-varying real term premium that changes sign. I find that changes in investors’ appetite for risk are an important source of variation in asset prices. In response to this shock, the term premium and the stock risk premium move in opposite directions. Real default-free bonds are good hedges against an increase in stock discount rates. When the level of stock discount rates is high, the bond risk premium and bond-stock correlations are negative (and vice versa). An empirical ICAPM with shocks to discount rates as a factor jointly prices the cross-section of bonds (by maturity) and stock portfolios (value, size, momentum).

Link: http://home.uchicago.edu/skozak/JMP.pdf

The author: Serhiy Kozak, Booth School of Business and Department of Economics, University of Chicago http://home.uchicago.edu/skozak/

The mechanism of the time variation in the correlation between the US stock market and long-term government bond returns are far less understood.

Correlation is a function of the covariance of returns and the respective volatilities.

We make this distinction to highlight the importance of the respective components – variance and covariance.

We use Campbell-Shiller (1988) decomposition as a theoretical framework to express unexpected stock and bond returns as components related to economic fundamentals.

Unexpected stock returns are decomposed into changing expectations of future real cash flow, future real short-term interest rates and the future excess returns on stocks.

Unexpected bond returns are decomposed into changing expectations of future inflation rates, future real short-term interest rates and future excess returns on long-term bonds (bond risk premium)

Since the variance and covariance of these components constitute the variance and covariance of stock and bond returns, we attempt to use time-varying comovement among the fundamental components to shed light on the economic mechanisms driving the time variation in the realised second moments of stock and bond returns.

1. Obtain time-series of expected values

Our novel approach consists of using survey forecast data from the BlueChip Economic Indicators survey to obtain a time-series of expected values for the fundamental components of the decomposition, namely cash flow, short-term interest rate and excess bond returns.

2. Calculate the time-series of unexpected values (news) of these components

3. We then use the DCC to describe the time-varying comovement among these news components and look at the extent to which these explain the variation in the second moments of stock and bond returns.

Other variables in the literature as being related to the stock-bond correlation:

  • Time variation in investors’ liquidity needs
  • Yield spread and short term nominal rate
  • Flight-to-quality: rising stock market uncertainty


The aim of this paper is to empirically examine the economic mechanisms underlying the correlation of stock and bond returns. Using a Campbell-Shiller decomposition we express unexpected stock and bond returns into news components related to macroeconomic fundamentals. The variance and covariance of these news components constitute the variance and covariance of stock and bond returns. We therefore attempt to use time-varying co- movement among the innovations to shed light on the economic mechanisms driving the time variation in the realised second moments of stock and bond returns. Using survey forecast data for the macroeconomic components we show that the uncertainty in cash flow and excess stock returns is able to explain the variation in excess stock variance up to an R2 of 24%. The variation in excess bond variance can be attributed to the uncertainty in real short-term interest rates and excess bond returns up to an R2 of 16%. As for the covariance between stock and bond returns, it is determined by the interaction between several of the macroeconomic news components and we are able to account for up to 24% of the variation. Our findings highlight the importance of the interaction between cash flow news and inflation news for negative stock-bond correlation.


The economic forces that drive the prices of stocks and bonds, as well as the comovement between the prices of stocks and bonds are discussed in two parts on the FRBSF Economic Letter on 1996. The part I discusses the relationship between the movements in the stock and bond markets at the macroeconomic aggregate level; the part II discusses it at the microeconomic firm level.

Part I – on the relation between stocks and bonds at the macroeconomic aggregate level

The present value model is discussed, which is as the framework for understanding how the prices of stocks and bonds are determined. According to the present value model, their current prices should be equal to the present value of future cash flows, subject to the appropriate discount rates, which consist of the real interest rate, inflation expectations, and a premium for holding a risky asset.

The article reviewed Shiller and Beltratti’s 1992 paper “stock prices and bond yields – can their comovements be explained in terms of present value models?”. Their study shows that:

  • the theoretical correlation between stock and long-term bond returns under the premise of the present value model is a mere 0.06.
  • While the observed correlation between stock and long-term bond returns is 0.37, small in economic terms but higher than expected theoretical rate.
  • One explanation for the differences is that the stock market overreacts to the bond market, or vice versa. Overreaction here implies something “irrational” in the behaviour of financial markets.

The article also reviewed the paper by Campbell. and Ammer (1993) regarding to what moves stock and bond markets. They focus on the excess returns and break them into components associated with “news” about future cash flows, thus dividends for stocks and coupons for bonds, and “news” about future discount rates, thus real interest rate, inflation expectations, risk premiums etc. “News” here refers to surprises, the unexpected component.

Campbell. and Ammer (1993) find that:

For stock excess returns

  • about 70% of the variance of excess stock returns was attributable to the “news” about future risk premiums for holding stocks;
  • about 15% of the stock return variance was attributable to “news” about future dividends
  • real interest rates plays a relatively minor role in the variation of stock returns
  • inflation plays a even less role

For bond excess returns

  • almost all the variation in bond returns can be accounted for by news about future inflation
  • also news about future risk premiums for holding bonds and news about future inflation are found to have offsetting effects on bond price variability (or negatively correlated) because the capital loss from higher expected inflation is partly offset by a capital gain from lower expected future bond returns.

They also reported that over the full sample 1952-1979, the two asset returns had a modest positive correlation of 0.20. The low correlation is due to the balance among several offsetting factors

  • stock and bond returns tend to move in opposite directions when expected future inflation varies (rising long-run expected inflation is bad news for the bond market but good news for the stock market
  • 1973-1987, real interest rate changes tended to result in stock and bond returns moving in the same direction
  • stock and bond returns move in the same direction when expected future risk premiums for holding stocks and bonds change.

Part I – on the relation between stocks and bonds at the microeconomic firm level


Link: http://www.frbsf.org/economic-research/publications/economic-letter/1996/june/on-the-relation-between-stocks-and-bonds-part-i/