For repeated with the data from 1963 to

For a long time, the
ability of CAPM and consumption CAPM, (C)CAPM afterwards, were in doubt. The
reason was that these two models performed poorly on explaining the stock
returns with different characteristics, such as size and book-to-market. For
example, they fail to predict that value stocks have higher returns than growth
stocks in general. Previous studies show that it is due to the model’s premise
that the risk premia are constant over time. However, Lettau and
Ludvigson(2001) brought hope back to (C)CAPM demonstrating that if the models are
used with the right scaling factor, their performances are significantly
improved, since it helps the models to capture the variance of risk of assets. The
authors chose consumption-wealth ratio, cay, as their conditioning variable considering
its strong forecasting ability for returns since it sums up the investors’
expectations on future returns.

The question arises then whether (C)CAPM scaled by cay can also
explain other abnormal returns. Therefore, in this
paper we examine the ability of scaled CCAPM to explain the currency trade
returns. Currency trade returns means the return that investors can earn by
investing in a currency with high-interest-rate while funding in a
low-interest-rate currency. In contrast to what uncovered interest parity
states. According to uncovered interest parity, this indicates the presence
of arbitrage because the exchange rate should already capture the difference of
the interest rates between two currencies.

The objective of this paper is to replicate
the empirical evidence in Lettau and Ludvigson (2001) using the data from 1963 to
1998, the period chosen by the authors in the paper. In addition, the procedure
is repeated with the data from 1963 to 2016 in order to check the genuine validity
of the evidence. Lastly the ability of scaled (C)CAPM on explaining currency
trade returns is examined. This paper is structured as
follows. Section 2 describes the former studies about (C)CAPM and carry trade
return. Next Section 3 describes the data that
are used for the regressions and the empirical methods implemented. In
Section 4 the empirical results of the
regressions are shown. Section 5 presents conclusions.

 

 

1        
Theoretical
Background

The
capital asset pricing model developed by Sharpe (1964) and Lintner (1965),
which has market return as the only factor, seemed to be the key to understand
financial markets. For instance, Black, Jensen, and Scholes (1972) and Fama and
MacBeth (1973) show the ability of CAPM on explaining the cross-sectional
average returns using the stock market return data from 1926 to 1968. Yet not
long after, a few following studies state that the explanatory power of CAPM
disappears if the model is applied to the later market returns. Reinganum (1981)
and Lakonishok and Shapiro (1986) demonstrate that CAPM failed to justify the
returns for the period between 1963 and 1990. Furthermore, in the meantime,
several researches suggest that there are other factors that can explain the
stock market returns besides the market return, which was considered to be
sufficient risk factor in CAPM. For example, Banz (1981) provides evidence of
the negative relation between the size of firms and the returns, namely smaller
firms tend to generate higher stock returns than larger firms. In addition,
Stattman (1980) and Rosenverg et al (1985) uncover the positive relation
between the returns and book-to-market ratio of the equity. In other words, value
stocks tend to have higher returns than growth returns in general.

Following
the failure of CAPM, consumption CAPM was developed by Breeden (1979) as an intertemporal
extension of CAPM. Since the falling of CAPM was attributed to one of its
assumptions that the premia on the risk factor are constant rather than
conditional, Breeden (1979) allow the model to reflect stochastic investment
opportunities. In addition, instead of having market return as the risk factor,
consumption CAPM adopts aggregate real consumptions as its risk factor because it
captures the whole market portfolio better than the market return. Nonetheless,
Hansen and Singleton (1982) and Breeden at el (1989) report that there is no
evidence that CCAPM performs better than CAPM on explaining the return differences
between stocks with different firm size.

However,
Lettau and Ludvigson(2002) argue that the failure of (C)CAPM does not lie on
the models themselves, but on the way to implement them. They suggest that if
(C)CAPM are executed with an appropriate scaling factor, which captures
conditional risk premia well, their performances enhances significantly that
they do as well as Fama-French 3 factor model does. The criterion of the
authors on choosing the conditioning variable is the ability of summarizing
market participants’ prediction on the future returns. Consumption-wealth ratio
was selected because according to the authors, investors’ behavior discloses
lots of information about their expectations on the market. Furthermore, the
authors solved the problem that human capital, a part of consumption-wealth ratio,
is not observable by having cay as the proxy for the ratio. According to Lettau
and Ludvigson(2001), cay is defined as integration of log consumption, log asset
wealth, and log labor income. Additionally the authors demonstrate that cay is
able to predict the future flow of the consumption-aggregate wealth ratio.

 

 

Forward
premium puzzle was introduced by the authors such as Hansen and Hodrick(1980)
and Fama(1984) in the early 1980’s. According to Hansen and Hodrick(1980), the
simple efficient-market hypothesis is inconsistent with the stock market
returns from 1973, because it was found that current forward rate has no
important role in anticipating future spot rates. Moreover, they highlight that
investors can earn excess returns in general by exploiting the interest
difference between currencies. This is again against the uncovered interest
rate parity, it says that the coefficient of the differences on exchange rate
changes must be equal to 1, yet the empirical results show that the coefficient
is mostly smaller than 1 and sometimes even drops below zero.

To
explain the existence of carry trade return, Verdelhan(???)

 

 

 

2        
Data
and Econometric Specification

2.1       
Data Description

In
section 4.1, which demonstrates the explanatory power of CCAPM, the same data
sets are used as Lettau and Ludvigson(2001) do. For data on returns, quarterly
return on 25 portfolios that are built with regard to the size and the
book-to-market ratio of the assets. These returns were provided by Fama.
Moreover, data on cay were acquired from the website of Lettau. According to
Lettau, cay data from 1963 to 1998 was proxied as cay= c-0.3054a-0.5891y and as
cay = c-0.297479a-0.735506y-0.722305 for the period of from 1952 to 2016, where
a and y denote asset wealth and labor income, respectively. 

In
section 4.3, which examines the validity of CCAPM with the carry trade returns,
the returns of 6 portfolios formed according to the interests of the currencies
from 1983 to 2015(Lustig and Roussanov, 2011. The same data on cay was adopted.

 

2.2       
Empirical Method

  Throughout the whole paper, Fama-MacBeth
regression methodology suggested in Fama and MacBeth(1973) was used. The
methodology consists of two stages of regressions. In the first stage, a
time-series regression is executed for returns of each portfolio to obtain
betas of risk factor variables. Next in the second stage, one single regression
is run with the betas collected from the first stage as right-hand-side
variables and the means of portfolios as dependent variable. The results of the
second stage indicate the performance of asset pricing models on justifying the
returns.