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Table 4. Profitability of indirect property index trading rules based on out-of...

May 9, 2024

It seems there is no specific question asked by the student regarding the information provided from the OCR model. The student has only shared the context of a table from a research paper or study, which includes data on trading rules and forecasting models. Without a specific question, I cannot provide a step-by-step solution or key concept. If the student has a question about how to interpret the table, compare the models, calculate additional statistics, or any other inquiry related to the data provided, I would be happy to assist with that. Please provide a clear question related to the information given.

What is the average annual return achieved by following the trading rule of "Trade when forecast next return > 0.87% per month" using the ARMA(1,3) forecasting model for 1-step ahead?

Solution by Steps

step 1

Identify the monthly returns that are greater than 0.87% from the data provided

step 2

Calculate the average of these monthly returns. Let's denote the average monthly return as

\bar{r}_m

step 3

Convert the average monthly return to an annual return by compounding. The formula for annual return from monthly returns is

(1 + \bar{r}_m)^{12} - 1

step 4

Apply the formula from step 3 to the average monthly return calculated in step 2 to find the average annual return

Answer

The average annual return is

(1 + \bar{r}_m)^{12} - 1

, where

\bar{r}_m

is the average of monthly returns greater than 0.87% using the ARMA(1,3) model for 1-step ahead.

Key Concept

Compounding monthly returns to annual returns

Explanation

The average annual return is calculated by compounding the average monthly returns that exceed the specified threshold, which in this case is 0.87% per month.

Solution by Steps

step 1

To comment on the transmission of the monetary policy decision to the longer-term rates, we analyze the impulse response functions depicted in Img 1

step 2

We observe that the initial response of the 1-month yield to a one standard deviation shock is a sharp increase, which suggests a strong immediate impact of monetary policy on short-term rates

step 3

The response of the 1-year yield is less pronounced than that of the 1-month yield, indicating that the impact of monetary policy is somewhat mitigated as the maturity increases

step 4

The 5-year and 10-year yields show a more gradual and sustained decrease, with the 10-year yield having the smallest response, which implies that the effect of monetary policy diminishes with longer maturities

step 5

The confidence intervals represented by the dotted lines provide an estimate of the uncertainty around the impulse responses. A wider interval suggests more uncertainty in the response

1 Answer

The transmission of monetary policy decisions to longer-term rates is less pronounced than to short-term rates, with the effect diminishing as the maturity increases. The confidence intervals indicate the level of uncertainty around these responses.

Key Concept

Impulse response functions in a VAR model

Explanation

Impulse response functions describe how a variable, such as a Treasury yield, responds over time to a shock in another variable, in this case, the 1-month Treasury yield. The response diminishes with longer maturities, indicating that monetary policy has a more immediate and stronger effect on short-term rates than on long-term rates.

step 1

To interpret the Granger causality test results from Img 3, we examine the

x^{2}

statistics and the corresponding probability values for each exclusion

step 2

A low probability value (typically less than 0.05) suggests that the excluded variable does Granger-cause the dependent variable, rejecting the null hypothesis

step 3

For Table (A), the exclusion of the 1-year yield and the combined exclusion of all yields have probability values of 0.000, indicating that these variables Granger-cause the 1-month yield

step 4

For Table (B), the exclusion of the 1-month yield and the combined exclusion of all yields have probability values of 0.000, suggesting that the 1-month yield Granger-causes the 1-year yield

step 5

For Tables (C) and (D), the probability values are higher, indicating that there is not enough evidence to reject the null hypothesis for the exclusions listed

2 Answer

The Granger causality tests suggest that the 1-year yield Granger-causes the 1-month yield and the 1-month yield Granger-causes the 1-year yield. There is not enough evidence to suggest Granger causality for the other exclusions in the 5-year and 10-year yields.

Key Concept

Granger causality tests

Explanation

Granger causality tests determine whether one time series can predict another. A low p-value indicates that the excluded variable provides information about future values of the dependent variable, thus "Granger-causing" it.

step 1

To determine if one model outperforms the other in forecasting accuracy, we compare the RMSE, MAE, and MAPE values from Img 5 for the VAR(2) and VAR(11) models

step 2

Lower values of RMSE, MAE, and MAPE indicate better forecast accuracy

step 3

For the 1-month yield, the VAR(2) model has higher RMSE and MAPE values than the VAR(11) model, suggesting that the VAR(11) model performs better for this maturity

step 4

For the 1-year, 5-year, and 10-year yields, the VAR(2) and VAR(11) models have similar RMSE and MAE values, but the VAR(2) model has slightly lower MAPE values for the 1-year and 5-year yields

step 5

The overall performance of each model should be assessed by considering all three accuracy measures and the specific application context

3 Answer

The VAR(11) model outperforms the VAR(2) model for the 1-month yield based on RMSE and MAPE. For the other maturities, the differences in forecast accuracy are minimal, with the VAR(2) model having a slight edge in MAPE for the 1-year and 5-year yields.

Key Concept

Forecast accuracy comparison

Explanation

Forecast accuracy is assessed using measures like RMSE, MAE, and MAPE. Lower values indicate better performance. The choice between models may depend on which accuracy measure is most relevant for the application.

Solution by Steps

step 1

To assess market efficiency based on the results in Table 4, we need to compare the average annual returns of the trading strategies to the transaction costs and the buy and hold strategies

step 2

We consider the transaction cost of

1.7\%

per trade. With an approximation of 2 trades per year, the annual transaction cost would be

2 \times 1.7\% = 3.4\%

step 3

We compare the average annual returns from the trading strategies to the buy and hold strategies, taking into account the transaction costs. If the trading strategies yield higher returns even after accounting for transaction costs, it may suggest market inefficiency

step 4

We observe the highest average annual return from the trading strategies is

9.26\%

for the VAR(4) 1 step ahead under the rule "Trade when forecast next return positive"

step 5

Subtracting the transaction cost from the highest trading strategy return:

9.26\% - 3.4\% = 5.86\%

step 6

We compare this net return to the buy and hold strategies:

8.07\%

for equities and

2.50\%

for treasury bills

step 7

The net return from the best trading strategy (5.86%) is lower than the buy and hold equities strategy (8.07%) but higher than the treasury bills (2.50%)

Answer

The results in Table 4, after accounting for transaction costs, do not provide strong evidence of market inefficiency since the net return from the best trading strategy is lower than the buy and hold equities strategy. However, it does suggest that the trading strategy outperforms the treasury bills, even after transaction costs.

Key Concept

Market Efficiency and Trading Strategy Returns

Explanation

A market is considered inefficient if a trading strategy can yield abnormal profits after accounting for transaction costs. In this case, the best trading strategy does not outperform the buy and hold equities strategy, suggesting no strong evidence of market inefficiency.

Solution by Steps

step 1

To derive the representation

\Delta \mathbf{Y}_t = \Pi \mathbf{Y}_{t-1} + \epsilon_t

, we first define

\mathbf{Y}_t \equiv \left[ y_{1t}, y_{2t} \right]^\prime

step 2

We take the first differences of the given equations to obtain

\Delta y_{1t}

and

\Delta y_{2t}

. This involves subtracting

y_{1t-1}

and

y_{2t-1}

from both sides of the equations respectively

step 3

We express

v_t

and

w_t

in terms of

y_{1t}

and

y_{2t}

using the given system of equations and then substitute

v_{t-1}

and

w_{t-1}

in terms of

y_{1t-1}

and

y_{2t-1}

step 4

We then combine the first differences and the expressions for

v_t

and

w_t

to express

\Delta \mathbf{Y}_t

in terms of

\mathbf{Y}_{t-1}

and the white noise processes

\epsilon_{1t}^*

and

\epsilon_{2t}^*

step 5

The matrix

\Pi

and the vector

\epsilon_t

are then identified by comparing the resulting expression with the target representation

\Delta \mathbf{Y}_t = \Pi \mathbf{Y}_{t-1} + \epsilon_t

1.1 Answer

The entries of

\Pi

and

\epsilon_t

are functions of the parameters

\delta, \eta, \rho_1, \rho_2

and the white noise processes

\epsilon_{1t}^*, \epsilon_{2t}^*

as derived in the steps above.

step 6

To ensure

\mathbf{Y}_t

is a cointegrated process, we choose

\rho_1

and

\rho_2

such that 0 < \rho_i < 1 for

i=1,2

, which implies that both

v_t

and

w_t

are stationary processes

step 7

We then use the definition of cointegration, which requires that a linear combination of

y_{1t}

and

y_{2t}

is stationary, even if the individual series are not

step 8

We express

\Pi

in terms of

\alpha

and

\beta

by identifying the cointegrating vector

\beta

and the adjustment coefficients

\alpha

from the stationary linear combination of

y_{1t}

and

y_{2t}

step 9

The matrix

\Pi

is then rewritten as

\Pi = \alpha \beta'

by substituting the derived values of

\alpha

and

\beta

into the representation

1.2 Answer

The matrix

\Pi

can be rewritten as

\Pi = \alpha \beta'

with the derived values of

\alpha

and

\beta

ensuring that

\mathbf{Y}_t

is a cointegrated process.

Key Concept

Deriving the representation of a bivariate process in terms of its parameters and white noise processes, and ensuring cointegration by choosing appropriate values for the parameters.

Explanation

The steps show how to manipulate the given system of equations to derive the required representation and to ensure cointegration by choosing parameters that result in a stationary linear combination of the time series.